TRIGONOMETRY HELP PLEASE!!!!!!?

1. sin 75(degrees) cos 15(degrees) - cos 75(degrees) sin 15(degrees)
= sin (75-15)
= sin 60
2. if x is an acute angle, and cos x = 4/5, then cos 2x is equal to?
cos 2x=cos^2 x - sin^2 x
=(4/5)^2-(3/5)^2
=16/25-9/25
=7/25
3. If sin x = root 5/ 3, then cos 2x equals?
sin x = root 5/3
opp=root 5
hyp = 3
adj^2 = 3^2-(root 5)^2=9-5=4
adj=2
cos x = 2/3
cos 2 x = cos^2 x- sin^2 x=(2/3)^2-(root5/3)^2=4/9-5/9=-1/9


4. If tan A = 8 and tan B= 1/2, what is the value of tan (A + B)
tan (A+B)=tan A tan B/(1-tan A tan B)
= 8*1/2/(1-8*1/2)=4/(1-4)=-4/3

5. The expression sin (180-x) is equivalent to
sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
sin(180-x) = sin(180)cos(x) - cos(180)sin(x)=0-(-1)sin x=sin x


6. The expression sin A cos A + sin 2A is equivalent to
1/2 sin 2A+sin 2A=3/2 SIN 2A=3/2(2 SIN A COS A)=3 SIN A COS A


7. If x is an acute angle such that sinx = 5/13, what is the value of sin 2x
OPP=5
HYP=13
ADJ=ROOT(13^2-25)=ROOT(169-25)=12
COS X = 12/13
SIN 2X=2SINXCOSX=2*5/13*12/13=120/169

8. Which expression is equivalent to sin 22(degrees) cos 18(degrees) + cos 22(degrees) sin 18 (degrees)
SIN(22+18)=SIN 40

A slide has an angle of elevation of 25 degrees. It is 60 feet from the end of the slide to the stairway beneath the top of the slide. About how long is the slide?

Trigonometry is a branch of arithmetic that analyze triangles and the relationships between their facets and the angles between those facets. Trigonometry defines the trigonometric applications, which describe those relationships and have applicability to cyclical phenomena, alongside with waves. the sphere developed throughout the time of the 0.33 century BC as a branch of geometry used extensively for astronomical analyze.[2] it is likewise the inspiration of the smart artwork of surveying.

60

Next time, please post 1 question per question.

1. that is an identity for sin(75 - 15), or sin60
2. first, you have to find that the sine is 3/5. Then it is easy:

cos2x = cos(x + x) = cosx * cosx - sinx * sinx = 4/5 * 4/5 - 3/5 * 3/5 = 16/25 - 9/25 = 7/25

3. cosine is 2/3

cos2x = cos(x + x) = cosx * cosx - sinx * sinx = 2/3 * 2/3 - v''5/3 * v''5/3 = 4/9 - 5/9 = -1/9

4. (tanA + tanB) / 1 - (tanA * tanB) = (8 + 1/2) / 1 - (8 * 1/2) = 17/2 / (1 - 4) = 17/2 / -3 = 17/2 * 1/-3 = 17 / -6 = -17/6

5. I think it is -cosx, but I am not sure
6. assuming "sin2 A" means "sin^2 A", the answer is sin A (cosA + sin A)
7. cosine = 12/13
sin2x = sinx * cosx + cosx * sinx = 5/13 * 12/13 + 12/13 * 5/13 = 2 * 5/13 * 12/13 = 120 / 169
8. sin(22 + 18), aka sin4