In this worksheet, we will practice finding the value of a trigonometric function from a given value of another trigonometric function.
Q1:
True of False: If sin𝜃=35 and cos𝜃<0, then tan𝜃=−34.
Q2:
Find sin𝐵 given tan𝐵=43 and cos𝐵=35.
Q3:
Find tan𝐴 given sin𝐴=0.5 and cos𝐴=√32.
Q4:
If cot(𝜃)=−43 and cos(𝜃)>0, find csc(𝜃).
Q5:
Find cot𝜃 given sin𝜃=35 where 90<𝜃<180∘∘.
Q6:
Given that cot(𝜃)=−32, where 𝜋2<𝜃<𝜋, evaluate sec(𝜃) without using a calculator.
Q7:
Given that sin(𝜃)=35 and 0<𝜃<𝜋2, evaluate cos(𝜃), tan(𝜃), sec(𝜃), csc(𝜃), and cot(𝜃).
Q8:
Find the value of seccsccot(𝜃)(𝜃)−(𝜃), given that 180<𝜃<270∘∘ and sin(𝜃)=−35.
Q9:
Find the value of cotcsctansec𝜃−𝜃𝜃−𝜃 given 𝜃∈3𝜋2,2𝜋 and sin𝜃=−45.
Q10:
Find the value of sincoscossin𝛼𝛽−𝛼𝛽, given tan𝛼=34 where 𝛼 is the smallest positive angle and tan𝛽=158 where 180<𝛽<270∘∘.
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