Topics
>
Precalculus>
Trigonometry>
Trigonometry Mixed Review: Part 1>
Trigonometry Mixed Review: Part 1 (1)Trigonometry Mixed Review: Part 1 (1)
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 9 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- Answered
- Review
-
Question 1 of 9
1. Question
Which of the following are labelled correctly?There can be more than one answerHint
Help VideoCorrect
Well Done!
Incorrect
Check each triangle and identify if the labels are correct
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as “opp”, but it should be hypThe side opposite of `theta` is labelled as “hyp”, but it should be oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled incorrectly
-
Question 2 of 9
2. Question
Solve for:`(i) \text(sin)theta``(ii) \text(cos)(90-theta)`
Enter fractions as: x/y-
`\text(sin)theta =` (3/5)
`\text(cos)(90 - theta) =` (3/5)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$`\text(Solving for) (i) sin theta`First we need to identify which trig ratio to use.One of the known lengths `(3)` is `\text(opposite)` to `theta` and the other length `(5)` is the `\text(hypotenuse)`
Hence, we can use the `sin \text(ratio)` to solve for `sintheta``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `cos theta` `=` $$\frac{\color{#004ec4}{3}}{\color{#e85e00}{5}}$$ Plug in the values `\text(Solving for) (ii) cos (90-theta)`First we need to understand which angle is `(90-theta)`.
Notice that the two known angles of the triangle is the right angle `(90°)` and `theta`.
Hence, the other angle left is `(90-theta)`.Now, one of the known lengths `(3)` is `\text(adjacent)` to `(90-theta)` and the other length `(5)` is the `\text(hypotenuse)`
Hence, we can use the `cos \text(ratio)` to solve for `cos(90-theta)``cos (90-theta)` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (90-theta)` `=` $$\frac{\color{#00880a}{3}}{\color{#e85e00}{5}}$$ Plug in the values `sintheta=3/5``cos (90-theta)=3/5` -
`\text(sin)theta =` (3/5)
-
Question 3 of 9
3. Question
Solve for `x` if:`theta=30`
- `x=` (60)`°`
Hint
Help VideoCorrect
Excellent!
Incorrect
The sum of the interior angles of a triangle is `180` degrees.
Identify the known values
`theta=30°``\text(right angle)=90°`To solve for `x`, we need to subtract the total value of the known angles from `180` degrees`x` `=` `180°-(``theta``+``\text(right angle)``)` `=` `180°-(``30°``+``90°``)` Plug in the values `=` `180°-120°` Evaluate `x` `=` `60°` `x=60°` -
Question 4 of 9
4. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (37)`°`
Correct
Keep Going!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(16)` is `\text(adjacent)` to `theta` and the other length `(20)` is the `\text(hypotenuse)`
Hence, we can use the `cos \text(ratio)` to solve for `theta``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos theta` `=` $$\frac{\color{#00880a}{16}}{\color{#e85e00}{20}}$$ Plug in the values `cos theta` `=` `0.8` Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(-1) (0.8)` The inverse of `cos` is `cos^(-1)` `theta` `=` `36.869°` Use the `\text(shift) cos` function on your calculator `theta` `=` `37°` Rounded to the nearest degree `theta=37°` -
Question 5 of 9
5. Question
Solve for `y`
Round your answer to two decimal places- `y =` (9.41)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(65°)` has `y` as an `\text(adjacent)` side and the other length `(18)` is the `\text(hypotenuse)`
[add purple angle fill for `65°`]Hence, we can use the `cos \text(ratio)` to solve for `y``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (65°)` `=` $$\frac{\color{#00880a}{y}}{\color{#e85e00}{18}}$$ Plug in the values Get `y` by itself to find its value`cos (65°)` `=` `y/18` `18 xx cos (65°)` `=` `y` Multiply both sides by `18` `18 xx 0.522` `=` `y` Evaluate `cos(65°)` on the calculator `9.41` `=` `y` Round to one decimal place `y` `=` `9.41` `y=9.41` -
Question 6 of 9
6. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (39)`°`
Correct
Excellent!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(11)` is `\text(adjacent)` to `theta` and the other length `(9)` is `\text(opposite)` to `theta`
Hence, we can use the `tan \text(ratio)` to solve for `theta``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan theta` `=` $$\frac{\color{#004ec4}{9}}{\color{#00880a}{11}}$$ Plug in the values `tan theta` `=` `0.818` Use the inverse function for `tan` on your calculator to get `theta` by itself`theta` `=` `tan^(-1) (0.818)` The inverse of `tan` is `tan^(-1)` `theta` `=` `39.2831°` Use the `\text(shift) tan` function on your calculator `theta` `=` `39°` Rounded to the nearest degree `theta=39°` -
Question 7 of 9
7. Question
Solve for `x`
Round your answer to two decimal places- `x =` (7.61)
Hint
Help VideoCorrect
Correct!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(43°)` has `x` as an `\text(opposite)` side and `9.5` as an `\text(adjacent)` side
Hence, we can use the `tan \text(ratio)` to solve for `x``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan (43°)` `=` $$\frac{\color{#004ec4}{x}}{\color{#00880a}{9.5}}$$ Plug in the values Now we need to have `x` on one side of the equation`tan (43°)` `=` `x/9.5` `9.5 times tan (43°)` `=` `x` Multiply both sides by `9.5` `9.5 times 0.801` `=` `x` Evaluate `tan (43°)` on the calculator `7.61` `=` `x` Round to two decimal places `x` `=` `7.61` `x=7.61` -
Question 8 of 9
8. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (55)`°`
Correct
Nice Job!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(12)` is `\text(adjacent)` to `theta` and the other length `(21)` is the `\text(hypotenuse)`
Hence, we can use the `cos \text(ratio)` to solve for `theta``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos theta` `=` $$\frac{\color{#00880a}{12}}{\color{#e85e00}{21}}$$ Plug in the values `cos theta` `=` `0.5714` Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(-1) (0.5714)` The inverse of `cos` is `cos^(-1)` `theta` `=` `55.152°` Use the `\text(shift) cos` function on your calculator `theta` `=` `55°` Rounded to the nearest degree `theta=55°` -
Question 9 of 9
9. Question
Solve for `b`
Round your answer to two decimal places- `b =` (119.06)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(26°25′)` has `48` as an `\text(opposite)` side and the other length `b` is the `\text(hypotenuse)`
Hence, we can use the `sin \text(ratio)` to solve for `b``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `sin (26°25′)` `=` $$\frac{\color{#004ec4}{48}}{\color{#e85e00}{b}}$$ Plug in the values Get `b` by itself to find its value`sin (26°25′)` `=` `48/b` `b xx sin (26°25′)` `=` `48` Multiply both sides by `b` `b` `=` `(48)/(sin (26°25′))` Divide both sides by `sin (26°25′)` `b` `=` `(48)/(0.403)` Evaluate `sin(26°25′)` on the calculator `b` `=` `119.06` Round to two decimal places `b=119.06`
Quizzes
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)