Trignometry

5sin thita +12cos theta=13 then find the value of 5cos thita -12sin theta

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. First, the name of θ is "theta" not "thita"

(5sinθ + 12cosθ)^2 = 169
25sin^2θ + 120sinθcosθ + 144cos^2θ = 169

(5cosθ - 12sinθ)^2 = 25cos^2θ - 120sinθcosθ + 144 sin^2θ
= 25cos^2θ - (169-25sin^2θ-144cos^2θ) + 144sin^2θ
= 25(cos^2θ+sin^2θ) + 144(sin^2θ+cos^2θ) - 169
= 25+144-169
= 0

or,
5sinθ + 12cosθ
= 13(5/13 sinθ + 12/13 cosθ)
now let x be the angle such that sinx = 12/13 and cosx = 5/13
= 13sin(θ+x)
So, we have
13sin(x+θ) = 13
sin(x+θ) = 1
Now, we also have
5cosθ - 12sinθ = 13(5/13 cosθ - 12/13 sinθ)
= 13cos(x+θ)
since sin(x+θ) = 1, cos(x+θ) = 0 as above

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
oobleck

Similar Questions

1. Math

1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta). 2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta)

2. Algebra2

The function f(theta) and g (theta) are sine functions where f(0)=g(0)=0. The amplitude of f (theta) is twice the amplitude of g(theta). The period of f(theta) is one-half the period of g(theta). If g (theta) has a period of 2pi

3. Pre-Calculus

Which is the polar form of the parametric equations x=5cos(theta) and y=5sin(theta) ? a. r= 5(theta) b. r= 5 c. r= 25 cos (theta) sin (theta)***** d. r= 25cos^2 (theta) + 25sin^2 (theta) Which is the polar form of the parametric

4. Trigonometry

Let (7,-3) be a point on the terminal side of theta. Find the exact values of cos of theta, sec of theta and cot of theta?

1. Math

Let (7,-3) be a point on the terminal side of theta. Find the exact values of sin of theta, csc of theta and cot of theta?

2. calculus

let theta be an angle of quadrant IV such that sin theta = -8/9 find the exact value of sec theta and cot theta?

3. math

Let theta be an angle in quadrant IV such that sin(theta)=-(2)/(5). Find the exact values of sec(theta) and tan(theta).

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.)

1. trig

If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.

2. math;)

What is a simplified form of the expression (sec^3 theta) - (sec theta/cot^2 theta)? a. 0 b. sec theta-tan theta c. cos theta d. sec theta***** Every time I attempt to work out this problem I end up with one. I know the answer is

3. math;)

Julia wants to simplify the term sec^2 theta-1/cot^2 theta+1 in a trigonometric identity that she is proving. Which of the following identities should use to help her? Select all that apply. (2 ANSWERS) a. sin^2 theta+cos^2

4. trig

Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the exact value of tan(theta) and cos(theta).