Question

If cos theta =0.8 and sin theta =0.3, then tan(-theta)=

Answer 1

We can use the fact that tan(-θ) = -tan(θ) to find the value of tan(-θ) from the given values of cos(θ) and sin(θ). First, we can use the Pythagorean identity to find the value of cos²(θ) + sin²(θ):

cos²(θ) + sin²(θ) = (0.8)² + (0.3)² = 0.64 + 0.09 = 0.73

Now, we can use the fact that cos²(θ) + sin²(θ) = 1 to find the value of cos(-θ) and sin(-θ):

cos(-θ) = cos(θ) = 0.8

sin(-θ) = -sin(θ) = -0.3

Finally, we can use the definition of tangent as the ratio of sine to cosine to find the value of tan(-θ):

tan(-θ) = -tan(θ) = -(sin(θ) / cos(θ)) = -0.3 / 0.8 = -0.375

Therefore, tan(-θ) = -0.375.

Explanation: