find the exact value of a) cos 77 b) sin120 c) tan 105 d) sin 15?

Question

can some1 please remind me hw to do that. i did it a while ago bt amkinda rusty now. thanx

sorry a) is cos75 not cos 77

Answer 1

a) cos(75) = cos(30+45) = cos(30)cos(45) - sin(30)sin(45)
b) sin(120) = sin(90+30) = sin(90)cos(30) + cos(90)sin(30)
c) tan(105) = tan(60+45) = sin(60+45)/cos(60+45)
= [sin(60)cos(45)+cos(60)sin(45)] / [cos(60)cos(45) - sin(60)sin(45)]
d) sin(15) = sin(45-30) = sin(45)cos(30) - cos(45)sin(30)

Then use sin(45)=cos(45)=sqrt(2)/2
sin(30)=cos(60)=1/2
sin(60)=cos(30)=sqrt(3)/2

Identities used:
sin(A+B)=sin A cos B + cos A sin B
cos(A+B)=cos A cos B - sin A sin B
sin(A-B)=sin A cos B - cos A sin B
cos(A-B)=cos A cos B + sin A sin B

Answer 2

If sin(?) = a million/6, then you definately understand two sides of the triangle -- the edge opposite the perspective, and the hypotenuse. the different edge is a million, and the hypotenuse is 6. utilising the pythagorean theorem (a^2 + b^2 = c^2), you are able to confirm that the third edge -- the only adjacent to the perspective -- is ?35. The secant is the hypotenuse (6) over the adjacent edge (?35), which might make sec(?) = 6/?35. in case you prefer to rationalize the denominator, it may be sec(?) = 6?35 / 35

Answer 3

a) .9217512697
b) .5806111842
c) 4.027801764
d) .6502878402

Buy an expensive calculator like a TI-84 Plus Silver Edition. All I had to do was press buttons.