**Inverses of sin cos and tan :**

Inverses of sin, cos and tan functions takes the ratio of corresponding functions and gives the angle θ.

Before going to see example problems first let us remember the following table

By knowing the relationship in the table, we can easily memorize the above table.

sin 0° = cos 90° = 0

sin 90° = cos 0° = 1

sin 30° = cos 60° = 1/2

sin 60° = cos 30° = √3/2

sin 45° = cos 45° = 1/√2

sin 0° = tan 0° = 0

**Example 1 :**

θ is an acute angle. Find the value of θ in degrees.

sin θ = √3/2

**Solution :**

To find the value of θ, we need to think about the angle for which we have the value √3/2.

In sin row we have √3/2 for the angle 60°.

Hence the value of θ is 60°.

**Example 2 :**

θ is an acute angle. Find the value of θ in degrees.

tan θ = √3

**Solution :**

To find the value of θ, we need to think about the angle for which we have the value √3.

In tan row we have √3 for the angle 60°.

Hence the value of θ is 60°.

**Example 3 :**

θ is an acute angle. Find the value of θ in degrees.

cos θ = √2/2

**Solution :**

To find the value of θ, we need to think about the angle for which we have the value √2/2.

In the table we don't have the value √2/2. So let us simplify the given value.

√2/2 (multiplying the numerator and denominator by √2) = (√2/2) x (√2/√2) ==> 2/2√2 ==> 1/√2

cos θ = 1/√2

In cos row we have 1/√2 for the angle 45°.

**Example 4 :**

θ is an acute angle. Find the value of θ in degrees.

sin θ = √2/2

**Solution :**

To find the value of θ, we need to think about the angle for which we have the value √2/2.

In the table we don't have the value √2/2. So let us simplify the given value.

√2/2 (multiplying the numerator and denominator by √2) = (√2/2) x (√2/√2) ==> 2/2√2 ==> 1/√2

sin θ = 1/√2

In sin row we have 1/√2 for the angle 45°.

**Example 5 :**

θ is an acute angle. Find the value of θ in degrees.

cos θ = √3/2

**Solution :**

To find the value of θ, we need to think about the angle for which we have the value √3/2.

From the relationship we know that the value of sin 30° is equal to the value of cos 60°. Like that the value of sin 60° is equal to the value of cos 30°.

in the sin row we have the value √3/2 for sin 60°. So, for cos 30° we will have the same value.

Hence the value of θ is 30°.

After having gone through the stuff given above, we hope that the students would have understood "Inverses of sin cos and tan".

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