Grade 12 Trigonometric Ratios Worksheet

A Grade 12 math worksheet focusing on the six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent, with application to right-angled triangles.

Grade 12 Math TrigonometryTrigonometric Ratios Sin, Cos, Tan, Csc, Sec and Cot

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Includes

Fill in the BlanksMultiple ChoiceShort AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.C.6CCSS.MATH.CONTENT.HSG.SRT.C.7CCSS.MATH.CONTENT.HSG.SRT.C.8

Topics

TrigonometryTrigonometric RatiosSineCosineTangentCosecantSecantCotangentRight Triangles

6 sections · Free to use · Printable

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Grade 12 Trigonometric Ratios

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Read each question carefully and provide the most accurate answer. Show all your work for full credit. Remember SOH CAH TOA for the primary trigonometric ratios and their reciprocals for the secondary ratios.

1. In a right-angled triangle, the sine of an angle is the ratio of the side to the hypotenuse.

2. The reciprocal of the cosine ratio is the ratio.

3. If tan(θ) = opposite/adjacent, then cot(θ) = .

4. For an angle θ, sec(θ) = 1 / .

5. In a right triangle, if the opposite side is 3 and the adjacent side is 4, what is the value of sin(θ)?

3/5

4/5

3/4

4/3

6. Which of the following is equivalent to csc(θ)?

1/sin(θ)

1/cos(θ)

1/tan(θ)

sin(θ)/cos(θ)

7. For the right triangle below, find the values of sin(A), cos(A), tan(A), csc(A), sec(A), and cot(A).

sin(A) =

cos(A) =

tan(A) =

csc(A) =

sec(A) =

cot(A) =

8. A ladder leans against a wall, forming a 60° angle with the ground. If the base of the ladder is 5 feet from the wall, how long is the ladder? Round your answer to two decimal places.

9. The value of tan(90°) is undefined.

True

False

10. For any acute angle θ, sin(θ) is always greater than cos(θ).

True

False