If sin (x) = square2/2 what is cos (x) and tan (x)

We are given that s i n (x) = 1 2

. We can solve this equation for x by taking the sine inverse of both sides of the equation.

s i n - 1 (s i n (x)) = s i n - 1 (1 2)

Simplifying the left-hand side gives the following:

x = s i n - 1 (1 2)

Thus, x is the angle, such that

s i n (x) = 1 2.

In trigonometry, there are special angles that have well known trigonometric values, and one of these angles is 30°. For an angle of measure 30°, we have the following:

s i n (30 ∘) = 1 2 c o s (30 ∘) = √ 3 2

Since

s i n (30 ∘) = 1 2, we have that

s i n - 1 (1 2) = 30 ∘, so x = 30°.

As we just saw, c o s (30 ∘) = √ 3 2

. To find tan (30°), we will use the trigonometric identity that

t a n θ = s i n θ c o s θ

. Thus, we have the following:

t a n (30 ∘) = s i n (30 ∘) c o s (30 ∘) = 1 2 √ 3 2 = 1 2 ⋅ 2 √ 3 = 1 √ 3

We get that

t a n (30 ∘) = 1 √ 3

. Thus, all together, we have that if s i n (x) = 1 2, then

c o s (x) = √ 3 2 and t a n (x) = 1 √ 3

. We are given that s i n (x) = 1 2

. We can solve this equation for x by taking the sine inverse of both sides of the equation.

s i n - 1 (s i n (x)) = s i n - 1 (1 2)

Simplifying the left-hand side gives the following:

x = s i n - 1 (1 2)

Thus, x is the angle, such that s i n (x) = 1 2.

In trigonometry, there are special angles that have well known trigonometric values, and one of these angles is 30°. For an angle of measure 30°, we have the following:

s i n (30 ∘) = 1 2 c o s (30 ∘) = √ 3 2 Since s i n (30 ∘) = 1 2, we have that s i n - 1 (1 2) = 30 ∘, so x = 30°.

As we just saw, c o s (30 ∘) = √ 3 2

. To find tan (30°), we will use the trigonometric identity that t a n θ = s i n θ c o s θ

. Thus, we have the following:

t a n (30 ∘) = s i n (30 ∘) c o s (30 ∘) = 1 2 √ 3 2 = 1 2 ⋅ 2 √ 3 = 1 √ 3

Step-by-step explanation:

n trigonometry, the inverse sine function, denoted as

s i n - 1 x, is defined as the function that undoes the sine function. That is, s i n - 1 x is equal to the the angle, θ, such that s in θ = x, and s i n - 1 (s i n (θ)) = θ

. We can use this definition to determine the angle that corresponds to a specific sine value