Question

Sin^2 30°+sin^2 40°+sin^2 50°

Answer 1

во- первых, синус сорока градусов равен косинусу пятидесяти градусов, значит, сумма второго и третьего слагаемых по основному тригонометрич. тождеству равна 1, во- вторых, синус тридцати градусов равен о,5, а его квадрат 0, 25, поэтому ответом на Ваш пример

будет 1, 25.

Answer 2

To calculate the value of the expression sin^2 30° + sin^2 40° + sin^2 50°, we can use the trigonometric identity:

sin^2 θ + cos^2 θ = 1

Since sin^2 θ + cos^2 θ equals 1, we can rewrite sin^2 θ as 1 - cos^2 θ:

sin^2 θ = 1 - cos^2 θ

Now, we can rewrite the given expression using the identity:

sin^2 30° + sin^2 40° + sin^2 50° = 1 - cos^2 30° + 1 - cos^2 40° + 1 - cos^2 50°

Next, we need to find the values of cos 30°, cos 40°, and cos 50°. These can be calculated as follows:

cos 30° = √3/2 ≈ 0.866 cos 40° = √(3 + √3)/2 ≈ 0.766 cos 50° = √(3 - √3)/2 ≈ 0.500

Now, substitute these values back into the expression:

1 - (0.866)^2 + 1 - (0.766)^2 + 1 - (0.500)^2

Simplify the expression further:

1 - 0.7496 + 1 - 0.586756 + 1 - 0.25

Now add the values together:

= 0.2504 + 0.413244 + 0.75 = 1.413644

So, sin^2 30° + sin^2 40° + sin^2 50° is approximately equal to 1.413644.