use degree measure for your answers. use a calculator and round the results to one decimal place for (c) and (d)

(a) in triangle ABC, sin B = square root of 2 all over 2. What are the possible values for angle B?

my thought: since sin is positive in the first and second quadrant, I believe that it is 45 degrees and 135 degrees.

(b) in triangle DEF, cos E = square root of 2 all over 2. What are the possible values for angle E?

my thought: since cos is positive in the first and fourth quadrant, I believe that it is 45 degrees and 315 degrees. This answer, however, does not agree with book answer.

(c)In triangle GHI, sin H = 1/4. What are the possible values for angle H?

My thought: ? Book answer: 14.5 degrees or 165.5 degrees

(d) In triangle JKL, cos K= -2/3. What are the possible values for angle K?

My thought:? Book Answer: 131.8 degrees

a is right
b is 45. There is only one hundred eighty degrees in a triangle, so no angle can be 315.
c. Arc sin .25 = ?
d. Arc cos -.666 =?
I don't know what you mean by "book answer". You have to work out the arc sin/cos values.

y= -2sec4x +2. Sketch the graph include 2 full periods. Use a graphing utility to verify result

how doe's trignometry is effective in life

i need help with a coupple of problems can you help me?

Certainly! I'd be happy to help you with your problems. Please go ahead and ask your questions, and I'll do my best to assist you.