Question

Angles θ and * are angles in standard position such that:

sinθ = -3/5 and θ terminates in Quadrant III
tan* = -7/24 and * terminates in Quadrant II
Find sin(θ + *)
A. 117/125
B. 8/25
C. 4/5
D. 44/125

Answer 1

To find sin(θ + *), we can use the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B). Given sin(θ) = -3/5, θ terminates in Quadrant II, tan(*) = -7/24, and * terminates in Quadrant II, we can find sin(θ + *). Plugging in the values, sin(θ + *) = -44/125.

Step-by-step explanation:

To find sin(θ + *), we can use the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

First, let's find sin(θ) and sin(*).

Given that sin(θ) = -3/5 and θ terminates in Quadrant II, we know that sin(θ) is negative in Quadrant II. In Quadrant II, the only trigonometric function that is positive is sin. Therefore, sin(θ) = -3/5 and cos(θ) = -4/5 (using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1).

Similarly, given that tan(*) = -7/24 and * terminates in Quadrant II, we know that tan(*) is negative in Quadrant II. In Quadrant II, the only trigonometric function that is positive is cos. Therefore, cos(*) = 24/25 (using the Pythagorean identity cos^2(*) + sin^2(*) = 1).

Now we can substitute these values into the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B). So, sin(θ + *) = sin(θ)cos(*) + cos(θ)sin(*).

Plugging in the values, we get sin(θ + *) = (-3/5)(24/25) + (-4/5)(-7/24) = -72/125 + 28/125 = -44/125.