What is sin theta cos theta equal to?
What is sin theta cos theta equal to?
Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse . No matter the size of the triangle, the values of sin(θ) and cos(θ) are the same for a given θ, as illustrated below.
What is sin theta by 1 cos theta?
sinθ1+cosθ=cscθ−cotθ
What is sin theta?
In the context of a right angle, the sine function, written as sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse, or long side, of the triangle. sinθ=oppositehypotenuse.
What is the value of sin under root 2?
The exact value of arcsin(√22) arcsin ( 2 2 ) is π4 . The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from π to find the solution in the second quadrant.
What is sin 2 theta cos 2 theta?
Explanation: The answer is 1 , because sin2(−θ)=sin2θ and sin2θ+cos2θ=1 . Hopefully this helps!
What is the formula for sin theta?
The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse.
What is the sin of 2 theta?
The double angles sin(2theta) and cos(2theta) can be rewritten as sin(theta+theta) and cos(theta+theta). Applying the cosine and sine addition formulas, we find that sin(2theta)=2sin(theta)cos(theta).
How to solve sin(Theta) = (square root of 2)/2 sin(θ)?
Solve for? sin (theta)=- (square root of 2)/2 sin(θ) = − √2 2 sin (θ) = – 2 2 Take the inverse sine of both sides of the equation to extract θ θ from inside the sine. θ = arcsin(− √2 2) θ = arcsin (- 2 2)
How to find the values of sinθ and cosθ?
We must now determine the values of sinθ and cosθ. First, we must define cotθ: cotθ = adjacent opposite. Therefore, the side adjacent θ measures 1 + √2 and the side opposite measures 1. We will need to find the hypotenuse for sinθ and cosθ. Let y be the hypotenuse. By pythagorean theorem we have
What is the period of the sin(θ) sin function?
The period of the sin(θ) sin ( θ) function is 2π 2 π so values will repeat every 2π 2 π radians in both directions.
How do you find the value of arcsin – √2 2?
Take the inverse sine of both sides of the equation to extract θ θ from inside the sine. The exact value of arcsin(− √2 2) arcsin ( – 2 2) is − π 4 – π 4.
