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Let


because that is the range of the inverse cosine funcition.
Also,
![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3Dcos%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B5%5C%2Ccos%5C%2C%5Ctheta%3D4%7D)
Square both sides and apply the fundamental trigonometric identity:



But

which means

lies either in the 1st or the 2nd quadrant. So

is a positive number:
![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Ctherefore~~%5Cmathsf%7Bsin%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%3D%5Cdfrac%7B3%7D%7B5%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
(4,-1),(-2,3)
slope = (3 - (-1) / (-2 - 4) = -4/6 = -2/3
y = mx + b
slope(m) = -2/3
use either of ur points...(4,-1)...x = 4 and y = -1
now sub into the formula and find b, the y int
-1 = -2/3(4) + b
-1 = -8/3 + b
-1 + 8/3 = b
-3/3 + 8/3 = b
5/3 = b
so ur equation is : y = -2/3x + 5/3
Answer:
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1. SQ and VX
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Step-by-step explanation:
An Interior Angle is an angle inside a shape
Alternate exterior angles are the pair of angles that lie on the outer side of the two parallel lines but on either side of the transversal line.