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Sine, cosine and tangent
This test applies sine, cosine and tangent in right triangles. Tasks teach students to select the correct trigonometric ratio, find an unknown side or angle and use fundamental identities.
Questions: 12Estimated time: 18 minutes
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Question 1out of 12
sin α = 0.80 and α is acute. Use sin²α + cos²α = 1 to find cos α.
From sin²α + cos²α = 1, obtain cos α = √(1 − sin²α), taking the positive root because α is acute. Square the sine first.
Question 2out of 12
Calculate: sin 90° = ?
Find the required trigonometric function row and angle column. Their intersection contains the answer.
Question 3out of 12
Which special-angle trigonometric identity is correct?
Recall the special-angle values: sin 30° = 1/2, cos 60° = 1/2 and tan 45° = 1. Select the matching identity.
Question 4out of 12
sin α = 0.80, hypotenuse 50. Find the opposite side.
In a right triangle, sin α = opposite leg / hypotenuse. Divide the opposite leg by the hypotenuse for sine; multiply the hypotenuse by sin α to find the opposite leg.
Question 5out of 12
The adjacent side is 15 and hypotenuse 17. Find the cosine.
In a right triangle, cos α = adjacent leg / hypotenuse. The hypotenuse is opposite the right angle; the adjacent leg touches the selected acute angle.
Question 6out of 12
The opposite side is 32 and hypotenuse 68. Find the sine.
In a right triangle, sin α = opposite leg / hypotenuse. Divide the opposite leg by the hypotenuse for sine; multiply the hypotenuse by sin α to find the opposite leg.
Question 7out of 12
The opposite side is 21 and adjacent side 72. Find the tangent.
tan α = opposite leg / adjacent leg. Tangent relates both legs directly without using the hypotenuse. Use inverse tangent to find the angle.
Question 8out of 12
Calculate: cos 60° = ?
In the trigonometric table, find the cos row and the stated angle column. Their intersection contains the answer.
Question 9out of 12
Which trigonometric function directly relates the opposite side and hypotenuse?
In a right triangle, sin α = opposite leg / hypotenuse. Divide the opposite leg by the hypotenuse for sine; multiply the hypotenuse by sin α to find the opposite leg.
Question 10out of 12
Which special angle has sine approximately 0.87?
Compare the given value with the known sine values of the special acute angles. You can recall them from the special-angle table or derive them from the standard right triangles. Choose the angle whose sine is closest to the given decimal value.
Question 11out of 12
sin α = 0.60 and α is acute. Use sin²α + cos²α = 1 to find cos α.
From sin²α + cos²α = 1, obtain cos α = √(1 − sin²α), taking the positive root because α is acute. Square the sine first.
Question 12out of 12
Calculate: tan 60° = ?
In the trigonometric table, find the tan row and the stated angle column. Their intersection contains the answer.
Time left: 00:00:00
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Sample questions
- The opposite side is ___ and hypotenuse ___. Find the sine.
- The adjacent side is ___ and hypotenuse ___. Find the cosine.
- The opposite side is ___ and adjacent side ___. Find the tangent.
- sin α = ___, hypotenuse ___. Find the opposite side.
- Which special angle has sine approximately ___?
Sine, cosine and tangent
In a right triangle, for angle α, sin α = opposite/hypotenuse, cos α = adjacent/hypotenuse and tan α = opposite/adjacent.
Choosing a ratio
First identify the hypotenuse and determine which legs are opposite and adjacent to the selected angle. Choose the ratio containing the known and required sides. Use an inverse trigonometric function to find an angle and check the angle mode of the calculator.
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