Thursday

April 24, 2014

April 24, 2014

Posted by **Stacey grahaM** on Tuesday, May 4, 2010 at 9:35am.

Csc theta = 1+cot theta

- Trig -
**bobpursley**, Tuesday, May 4, 2010 at 10:03ammultipy both sides by sintheta

1=sinTheta+cosTheta

This is only possible at Theta=0, 90, 360

- Trig -
**MathMate**, Tuesday, May 4, 2010 at 10:11amReduce to sin and cosines:

1/sinθ=(sinθ+cosθ)/sinθ

Thus, if θ ≠ 0,π 2π ...

we get

sinθ+cosθ=1

Taking advantage of symmetry about π/4, where sinπ/4=cosπ/4, substitute θ=φ-π/4:

sin(φ-π/4)+cos(φ-π/4)=1

Expanding by sum/difference formulae,

sinφcosπ/4-cosφsinπ/4 + cosφcosπ/4+sinφsinπ/4=1

Since sinπ/4=cosπ/4, we cancel terms in cosφ to get

2sinπ/4 sinφ=1

φ=arcsin(sqrt(2)/2)=±π/4

θ=0 or π/2

The first value has been rejected since the beginning, so θ=π/2.

- Trig - correction -
**MathMate**, Tuesday, May 4, 2010 at 10:23amfrom

φ=arcsin(sqrt(2)/2)=π/4 or 3π/4 ± 2kπ

θ=φ-π/4=0 or π/2 ±2kπ

Since θ=0 has been rejected since the beginning, we are left with

θ=π/2 (for solution between 0 and 360)

**Related Questions**

trig - How do i solve this equation over the interval [0degrees,360) cot(theta)+...

trig - If sin theta is equal to 5/13 and theta is an angle in quadrant II find ...

trig - how do you solve cot theta divided by csc theta is equal to cos theta?

trig - Given csc theta= 4, cot theta < 0 Find the exact values of cos theta ...

trig - find an expression equivalent to sec theta sin theta cot theta csc theta

trig - If theta is the measure of an angle in standard position with the given ...

trig 30 - For csc^2 A-1/cot A csc A, what is the simplest equivalent trig ...

Algebra II - Verify that (sec theta/sin theta)(cot theta/csc theta) = csc theta ...

trig - solve the equation 2 tan^2(theta)sin(theta)-tan^2(theta)=0 interval[0,...

Trig - Given 2secant^2 (theta) + 1 = 5 secant (theta), solve for (theta), to the...