Express each of the following in terms of another angle between 0 degrees and 180 degrees
a. sin 50 degrees
b. sin 150 degrees
c. cos 45 degrees
d. cos 120 degrees
please explain to me how to answer this question you don't have to answer it , but please give me a hint. its something i have never learnt. just simple give me a hint.
Express each of the following in terms of the cosine of another angle between 0 degrees and 180 degrees:
a) cos 20 degrees b) cos 85 degrees c) cos 32 degrees
d) cos 95 degrees e) cos 147 degrees f) cos 106 degrees
My answer:
a) - cos 160 degrees b) - cos 95 degrees c) -cos 148 degrees
d) -cos 85 degrees e) - cos 33 degrees f) - cos 74 degrees
Textbook answer:
a) cos 340 degrees b) cos 275 degrees c) cos 328 degrees
d) cos 265 degrees e) cos 213 degrees f) cos 254 degrees
My question: I do understand that the cosine of 20 degrees and 340 degrees are equal; but why are the answers greater than 180 degrees even though I was instructed to express my answer as the cosine of another angle between 0 degrees and 180 degrees.
Hint:
Draw the four Quadrants on a graph
Draw line length 1 at 50 degrees up from the x axis
Draw line length 1 at 50 degrees up from the -x axis
sadme sine for 50 degrees and 180 - 50 degrees
so
sin 50 = sin 130
By the way there are multiple answers to these
for example
sin 50 = sin 130 = cos 40 = -cos130
Sure, I can give you a hint. One useful property to remember is the relationship between complementary angles. Complementary angles are two angles whose measures add up to 90 degrees. Now, consider how you can use this property to express an angle in terms of another angle between 0 and 180 degrees.
To express each of the angles in terms of another angle between 0 degrees and 180 degrees, you can use the trigonometric identities that relate angles to their complementary or supplementary angles. One such identity you can use is the complement identity for sine and cosine:
1. For angle A, sin(A) = sin(180 - A)
2. For angle A, cos(A) = cos(180 - A)
Using these identities, you can find the equivalent angles in terms of another angle between 0 degrees and 180 degrees.