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Math  /  Trigonometry

Question2] Given that cos⁡θ=38,f\cos \theta=\frac{3}{8}, f A] sin⁡(90∘−θ)\sin \left(90^{\circ}-\theta\right)

Studdy Solution

STEP 1

1. We are given cos⁡θ=38\cos \theta = \frac{3}{8}.
2. We need to find sin⁡(90∘−θ)\sin(90^\circ - \theta).
3. We will use trigonometric identities to solve the problem.

STEP 2

1. Use the complementary angle identity.
2. Substitute the given value of cos⁡θ\cos \theta.

STEP 3

Recall the complementary angle identity in trigonometry, which states:
sin⁡(90∘−θ)=cos⁡θ\sin(90^\circ - \theta) = \cos \theta

STEP 4

Substitute the given value of cos⁡θ\cos \theta into the identity:
sin⁡(90∘−θ)=cos⁡θ=38\sin(90^\circ - \theta) = \cos \theta = \frac{3}{8}
The value of sin⁡(90∘−θ)\sin(90^\circ - \theta) is:
38\boxed{\frac{3}{8}}

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