If tanè = 4 / 3, then sinè =
F. 3 / 4
G. 3 / 5
H. 4 / 5
J. 5 / 3
K. 5 / 4
tan0 and sin0
us always, draw a diagram.
Label one of the acute angles θ.
The side opposite is 4 and the side adjacent is 3.
(Note: the hypotenuse is not a side!)
The hypotenuse is 5, since 3^2+4^2=5^2
Now, review your trig definitions.
sinθ = opposite/hypotenuse = 4/5
Thank you Steve.
To find the value of sine (sinè), given the value of tangent (tanè), you can use the Pythagorean identity, which states that sin²è + cos²è = 1.
Since we are given the value of tangent (tanè = 4/3), we can use the identity tan²è + 1 = sec²è to find the value of secant (secè).
Rearranging the equation, sec²è = tan²è + 1. Plugging in the given value of tanè, we have sec²è = (4/3)² + 1 = 16/9 + 1 = 25/9.
Now, we know that sec²è = 25/9. Taking the square root of both sides, we find secè = ±5/3. However, since we are looking for the value of sine, which is positive in the first quadrant, we take the positive value, secè = 5/3.
Finally, we can use the relationship between sine, cosine, and secant: sinè = 1 / secè.
Plugging in the value of secè that we found, sinè = 1 / (5/3) = 3/5.
Therefore, the correct answer is G. 3/5.