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
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
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.