Trigonometric Ratios Worksheet

A Grade 10 math worksheet covering sine, cosine, tangent, cosecant, secant, and cotangent ratios in right-angled triangles.

Grade 10 Math TrigonometryTrigonometric Ratios Sin, Cos, Tan, Csc, Sec and Cot

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2 Short AnswerMultiple ChoiceFill in the Blanks

Standards

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

Topics

TrigonometryRight TrianglesSineCosineTangentCosecantSecantCotangent

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Trigonometric Ratios: Sin, Cos, Tan, Csc, Sec, Cot

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Read each question carefully and provide the best answer. Show all your work for full credit.

1. In a right-angled triangle, if θ is an acute angle, define the following trigonometric ratios in terms of the opposite, adjacent, and hypotenuse sides:

a) sin(θ) =

b) cos(θ) =

c) tan(θ) =

2. Define the reciprocal trigonometric ratios:

a) csc(θ) =

b) sec(θ) =

c) cot(θ) =

Use the right-angled triangle below to answer questions 3-4.

3. What is the value of sin(A)?

12/13

5/13

12/5

5/12

4. What is the value of cot(A)?

12/13

5/13

12/5

5/12

5. In a right-angled triangle, if the opposite side is 8 and the hypotenuse is 17, then sin(θ) = and csc(θ) = .

6. If cos(θ) = 3/5, and the adjacent side is 9, then the hypotenuse is and sec(θ) = .

7. A ladder leans against a wall, forming a 60-degree angle with the ground. If the base of the ladder is 5 feet from the wall, how long is the ladder? (Round to two decimal places)