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Why is 2 sin theta cos theta equal to sin 2theta?
because sin(2x) = 2sin(x)cos(x)
What is the exact value of cos theta if csc theta -4 with theta in quadrant III?
csc θ = 1/sin θ → sin θ = -1/4 cos² θ + sin² θ = 1 → cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4 In Quadrant III both cos and sin are negative → cos θ= -(√15)/4
What trigonometric value is equal to cos 62?
The solution is found by applying the definition of complementary trig functions: Cos (&Theta) = sin (90°-&Theta) cos (62°) = sin (90°-62°) Therefore the solution is sin 28°.
How do you simplify csc theta cot theta cos theta?
cosec(q)*cot(q)*cos(q) = 1/sin(q)*cot(q)*cos(q) = cot2(q)
If sin(36 plus theta) cos(16 plus theta) find theta?
cos(α) = sin(90° - α) → cos(16° + θ) = sin(90° - (16° + θ)) = sin(74° - θ) → sin(36° + θ) = cos(16° + θ) → sin((36° + θ) = sin(74° - θ) → 36° + θ = 74° - θ → 2θ = 38° → θ = 19° → θ = 19 °+ 180°n for n= 0, 1, 2, ...
How do you simplify tan theta cos theta?
Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?
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.
How do you simplify cos theta times csc theta divided by tan theta?
'csc' = 1/sin'tan' = sin/cosSo it must follow that(cos) (csc) / (tan) = (cos) (1/sin)/(sin/cos) = (cos) (1/sin) (cos/sin) = (cos/sin)2
De Morgan's law in complex number?
(Sin theta + cos theta)^n= sin n theta + cos n theta
What is the identity for tan theta?
The identity for tan(theta) is sin(theta)/cos(theta).
What is sin theta cos theta?
It's 1/2 of sin(2 theta) .
In which quardant are the terminal arms of the angle lie when sin thita is less then zero and cos thita is greater then zero?
The fourth Across the quadrants sin theta and cos theta vary: sin theta: + + - - cos theta: + - - + So for sin theta < 0, it's the third or fourth quadrant And for cos theta > 0 , it's the first or fourth quadrant. So for sin theta < 0 and cos theta > 0 it's the fourth quadrant
If cos and theta 0.65 what is the value of sin and theta?
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
Why is 2 sin theta cos theta equal to sin 2theta?
because sin(2x) = 2sin(x)cos(x)
Prove that sin theta power 8 - cos theta power 8 equal to sin sq Theta -cos sq x 1-sin sq Theta cos sq theta?
The equation cannot be proved because of the scattered parts.
What is the derivative of sin under root theta?
The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
What is sec theta - 1 over sec theta?
Let 'theta' = A [as 'A' is easier to type] sec A - 1/(sec A) = 1/(cos A) - cos A = (1 - cos^2 A)/(cos A) = (sin^2 A)/(cos A) = (tan A)*(sin A) Then you can swap back the 'A' with theta
