Question

Sin10a=-2/6 cos20a=?

Answer 1

Ответ:

Объяснение:

sin10a=-2/6=-1/3;

$cos20a=cos2*(10a)=1-2*sin^{2} (10a)=1-2*(-\frac{1}{3} )^{2} =1-\frac{2}{9}}=\frac{7}{9}$

Answer 2

To solve the equation sin(10a) = -2/6 and find cos(20a), we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1.

Let's begin by solving the equation sin(10a) = -2/6:

sin(10a) = -2/6 sin(10a) = -1/3

Now, we can use the inverse sine function (also known as arcsin or sin^-1) to find the value of 10a:

10a = arcsin(-1/3)

To determine the value of arcsin(-1/3), we can use a calculator or a trigonometric table. The approximate value is -19.47 degrees.

10a = -19.47 degrees

Now, let's find the value of cos(20a):

cos(20a) = cos(2 * 10a)

We can use the double-angle identity for cosine: cos(2θ) = cos^2(θ) - sin^2(θ)

cos(20a) = cos^2(10a) - sin^2(10a)

Since we know the value of sin(10a) = -1/3, we can substitute it into the equation:

cos(20a) = cos^2(10a) - (-1/3)^2

cos(20a) = cos^2(10a) - 1/9

To find the value of cos^2(10a), we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1:

cos^2(10a) = 1 - sin^2(10a)

cos^2(10a) = 1 - (-1/3)^2 cos^2(10a) = 1 - 1/9 cos^2(10a) = 8/9

Now, we can substitute this value back into the equation for cos(20a):

cos(20a) = 8/9 - 1/9 cos(20a) = 7/9

Therefore, cos(20a) is equal to 7/9.