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Trigonometric Ratios Worksheet

Explore trigonometric ratios (sin, cos, tan, csc, sec, cot) in right-angled triangles for Grade 8 math.

Grade 8 Math TrigonometryTrigonometric Ratios Sin, Cos, Tan, Csc, Sec and Cot
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Fill in the BlanksMultiple ChoiceShort AnswerTrue / FalseLong Answer

Standards

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

Topics

trigonometryratiossincostancscseccotright triangle
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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 short answer questions.

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

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

3. Tangent is defined as the ratio of the opposite side to the   side.

1. Which of the following ratios represents the cosecant of an angle?

a

Opposite / Hypotenuse

b

Adjacent / Hypotenuse

c

Hypotenuse / Opposite

d

Hypotenuse / Adjacent

2. If sin(θ) = 3/5, what is the value of csc(θ)?

a

3/5

b

5/3

c

4/5

d

5/4

For the right-angled triangle below, identify the following trigonometric ratios for angle A.

b = 8a = 6c = 10ABC

1. sin(A) =  

2. cos(A) =  

3. tan(A) =  

4. csc(A) =  

5. sec(A) =  

6. cot(A) =  

1. The value of tan(θ) can be greater than 1.

T

True

F

False

2. The cosecant function is the reciprocal of the sine function.

T

True

F

False

1. 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? (Draw a diagram and show your work)