Question

Evaluate each of the following without using a calculator or computer. Show your work.
a. sin(arcsin(1/2) + arcos(1/2))
b. sec(arccos(-√3/2))
c. arctan(tan(3π/4))
d. tan(arctan(3π/4))

Answer 1

use special triangles. Do you know the special triangle that involves the angles 60 and 30?

Answer 2

first construct the special triangle:

Answer 3

Lets start with arcsin. Arcsin means you want the angle from 1/2. If we refer to what sin is, it is the Opposite / Hypotenuse (SohCahToa). So it must be 1/2 Which angle corresponds to O/H or 1/2 ?? It is 30 DEGREES.

Answer 4

Same thing for Arccos(1/2). This angle is 60. Add 30+60. So you must now work out SIN(90). If you think about the SIN GRAPH. At 90 degrees (x value is 90 remember), the y value is???? The y value is 1. So Sin(90) = 1. FINAL ANSWER.

Answer 5

thats how you solve a. you should be able to solve the rest in the same procedure. however you seem to not be responding so until you respond im not giving you any further help