Trigonometric Ratios Worksheet
A Grade 10 math worksheet covering sine, cosine, tangent, cosecant, secant, and cotangent ratios in right-angled triangles.
Includes
Standards
Topics
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)
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