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If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate sin 2 θ

Sagot :

ashish4112119

Answer:

24/25

Step-by-step explanation:

sin 2 θ = 3÷25/8 =24/25

from web2calc

View image ashish4112119
altavistard

Answer:

24/25

Step-by-step explanation:

P(u, v) = (3, 4) describes a triangle:  One vertex is at the origin (0, 0) and the other at (3, 4).  According to the Pythagorean Theorem, 3^2 + 4^2 = 5^2, so we know the hypotenuse length is 5 units.

Recall that the sine function is defined as opp/hyp, which here is 4/5, and that the cosine function as adj/hyp, which here is 3/5.  

Finally, we'll apply the double angle formula sin 2x = 2 sinx cos x.

Substituting the values found above,              sin 2x = 2(4/5)(3/5) = 24/25.

The sine of 2x (where x is the smaller acute angle whose vertex is (0, 0) ) is 24/25.

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