It's easiest to show all of the work (explanations/identities), and x represents theta.
cosxcotx + sinx = cscx
cosx times cosx/sinx + sinx = csc x (Quotient Identity)
cosx2 /sinx + sinx = csc x (multiplied)
1-sinx2/sinx + sinx = csc x (Pythagorean Identity)
1/sinx - sinx2/sinx + sinx = csc x (seperate fraction)
1/sinx -sinx + sinx = csc x (canceled)
1/sinx = csc x (cancelled)
csc x =csc x (Reciprocal Identity)
- cos theta
Well, darling, if we square the first equation and the second equation, add them together, and do some algebraic magic, we can indeed show that a squared plus b squared equals 89. It's like a little math puzzle, but trust me, the answer is as sassy as I am.
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
sin(theta) = 15/17, cosec(theta) = 17/15 cos(theta) = -8/17, sec(theta) = -17/8 cotan(theta) = -8/15 theta = 2.0608 radians.
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
cos2(theta) = 1 so cos(theta) = ±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
No.
The question contains an expression but not an equation. An expression cannot be solved.
Cos theta squared
Well, darling, if we square the first equation and the second equation, add them together, and do some algebraic magic, we can indeed show that a squared plus b squared equals 89. It's like a little math puzzle, but trust me, the answer is as sassy as I am.
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1
cos(theta) = 0.7902 arcos(0.7902) = theta = 38 degrees you find complimentary angles
1
2
4*cos2(theta) = 1 cos2(theta) = 1/4 cos(theta) = sqrt(1/4) = ±1/2 Now cos(theta) = 1/2 => theta = 60 + 360k or theta = 300 + 360k while Now cos(theta) = -1/2 => theta = 120 + 360k or theta = 240 + 360k where k is an integer.
- cos theta