1) Find the exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8).
Answer: 3/5
2) Find the exact value of sin(-pi/6).
Answer: -1/2
Thanks
both are correct
which angle is coterminal with a -400°angle in standard position? A. 40 B. 80 C. 320 D. 400
to answer anonymous' ? i got C.320 the selection a.40 would only apply if it was a positive 400 angle instead of the negative
Solve the inequality. (Enter your answer using interval notation.)
1
x − 3
≤
8
5x + 3
To find the exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8), we can use the Pythagorean Identity.
Step 1: Draw a right triangle with the x-axis as the adjacent side, the y-axis as the opposite side, and the hypotenuse as the distance between the origin and the point (6,-8).
Step 2: We know that the adjacent side is 6 and the opposite side is -8 (going downwards).
Step 3: Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse^2 = adjacent^2 + opposite^2
hypotenuse^2 = 6^2 + (-8)^2
hypotenuse^2 = 36 + 64
hypotenuse^2 = 100
hypotenuse = 10
Step 4: Now, we can find the exact value of cos theta by dividing the length of the adjacent side by the hypotenuse:
cos theta = adjacent / hypotenuse
cos theta = 6 / 10
cos theta = 3 / 5
Therefore, the exact value of cos theta is 3/5.
To find the exact value of sin(-pi/6), we can use the unit circle.
Step 1: Recall that the unit circle is a circle with a radius of 1 centered at the origin (0,0) on the coordinate plane.
Step 2: Locate the angle -pi/6 on the unit circle. Since -pi/6 is in the fourth quadrant, the reference angle is pi/6 in the first quadrant. The corresponding point on the unit circle is (cos(pi/6), sin(pi/6)), which is (sqrt(3)/2, 1/2).
Step 3: Since we are dealing with a negative angle, the value of sin(-pi/6) will be the opposite of sin(pi/6) or -1/2.
Therefore, the exact value of sin(-pi/6) is -1/2.