Trigonometry question

Question

if Sin(48°)≈0.74 then with true identities find the following using this estimate

csc(48°)

cos(48°)

tan(48°)

cos(42°)

sin(42°)

tan(42°)

cot(42°)

Answer 1

then cos(42) = sin(48) = 0.74 <--- sine of acute angle equals cosine of the complement

For any angle T, the pythagorean trig identity says:

(sin T)^2 + (cos T)^2 = 1

Then for PARTICULAR angle T = t=48

[sin (t) ]^2 + [cos(t)]^2 = 1

[ 0.74 ]^2 + [ cos(t)]^2 = 1

0.5476 + [ cos(t)]^2 = 1

[cos(t)]^2 = 1 - 0.5476

cos (t) = sqrt(0.4524)

= 0.6726

So cos(48)= 0.6726 = sin(42)

The folowing table summarizes:

Angle Sine Cosine

----------------------------------------

48 0.74 is given 0.6726 <-- calculated by pythagorean trig identity

42 0.6726 0.74 is given

you can now find csc = 1/sin

sec = 1/cos

tan = sin/cos

cot = 1/tan = cos/sin

for both 48 and 42 degrees, which I will leave for you to do

with your calculator