Trigonometric Ratios Worksheet
Understand and apply trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent) 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. Round all answers to two decimal places where necessary.
1. The sine of an angle in a right triangle is the ratio of the length of the side to the length of the hypotenuse.
2. The tangent of an angle is the ratio of the length of the opposite side to the length of the side.
3. The cosecant is the reciprocal of the function.
4. The secant is the reciprocal of the function.
5. The cotangent is the reciprocal of the function.
Consider a right triangle with an angle θ. If the opposite side is 3 and the adjacent side is 4, what is the value of tan(θ)?
3/5
4/5
3/4
4/3
In a right triangle, if sin(θ) = 5/13, what is the value of csc(θ)?
5/13
13/5
12/13
13/12
1. For the right triangle shown below, calculate the sine, cosine, and tangent of angle A. (Round to two decimal places)
sin(A) =
cos(A) =
tan(A) =
2. For the same triangle above, calculate the cosecant, secant, and cotangent of angle A. (Round to two decimal places)
csc(A) =
sec(A) =
cot(A) =
1. The secant of an angle is always less than 1.
True
False
2. In a right triangle, the hypotenuse is always the longest side.
True
False
1. A ladder 10 meters long is leaning against a wall. If the base of the ladder is 6 meters from the wall, what is the sine of the angle the ladder makes with the ground?
2. An airplane takes off at an angle of 30 degrees from the ground. If the plane has traveled 500 meters along its flight path, how high is the airplane above the ground?