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

yes. we do proportions in probabilities.

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