Grade 9 Trigonometric Ratios Worksheet

A Grade 9 math worksheet covering sine, cosine, tangent, cosecant, secant, and cotangent ratios in right-angled triangles.

Grade 9 Math TrigonometryTrigonometric Ratios Sin, Cos, Tan, Csc, Sec and Cot

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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

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

Topics

trigonometrytrigonometric ratiossinecosinetangentcosecantsecantcotangentright trianglegrade 9

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

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Read each question carefully and answer to the best of your ability. Show all your work for full credit. Round your answers to two decimal places where necessary.

1. For the right-angled triangle below, identify the opposite side, adjacent side, and hypotenuse with respect to angle θ.

Opposite:

Adjacent:

Hypotenuse:

2. Complete the following definitions for a right-angled triangle:

a) Sine (sin θ) = Opposite /

b) Cosine (cos θ) = / Hypotenuse

c) Tangent (tan θ) = Opposite /

d) Cosecant (csc θ) = / Opposite

e) Secant (sec θ) = Hypotenuse /

f) Cotangent (cot θ) = Adjacent /

3. Consider a right-angled triangle with sides a = 3, b = 4, and hypotenuse c = 5. Let θ be the angle opposite side 'a'. Calculate the following ratios:

a) sin θ =

b) cos θ =

c) tan θ =

d) csc θ =

e) sec θ =

f) cot θ =

4. If tan A = 12/5, what is the value of sin A?

5/13

12/13

5/12

13/12

5. In a right-angled triangle, csc θ is the reciprocal of sin θ.

True

False

6. A ladder leans against a wall, forming an angle of 60° with the ground. If the base of the ladder is 3 meters from the wall, how long is the ladder? (Draw a diagram to help you).