Posted by Stacey grahaM on Tuesday, May 4, 2010 at 9:35am.
Solve the equation in the interval [0•,360•]
Csc theta = 1+cot theta
- Trig - bobpursley, Tuesday, May 4, 2010 at 10:03am
multipy both sides by sintheta
This is only possible at Theta=0, 90, 360
- Trig - MathMate, Tuesday, May 4, 2010 at 10:11am
Reduce to sin and cosines:
Thus, if θ ≠ 0,π 2π ...
Taking advantage of symmetry about π/4, where sinπ/4=cosπ/4, substitute θ=φ-π/4:
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
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 10:23am
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)
Answer this Question
More 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 - If theta is the measure of an angle in standard position with the given ...
- 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 30 - For csc^2 A-1/cot A csc A, what is the simplest equivalent trig ...
- Trig - Given 2secant^2 (theta) + 1 = 5 secant (theta), solve for (theta), to the...
- trig - Find all values of [theta] in the interval 0°<=X<= 360° that ...
- trig - solve the equation 2 tan^2(theta)sin(theta)-tan^2(theta)=0 interval[0,...