# If sin s =2/3 and cos s = √5 over 3 what are the values of the remaining four trigonometric functions of s?

As below

Given

Similarly,

Verification :

As per Pythagoras theorem,

L H S =

R H S =

Hence proved.

Other trigonometric functions :

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Given that sin(s) = 2/3 and cos(s) = √5/3, we can use the Pythagorean identity to find the value of cos(s) and then determine the remaining trigonometric functions.

**sin(s) = 2/3**: Given.**cos(s) = √5/3**: Given.**tan(s) = sin(s)/cos(s)**: Substitute the given values into the formula to find tan(s). tan(s) = (2/3) / (√5/3) = 2/√5.**csc(s) = 1/sin(s)**: Reciprocal of sin(s). csc(s) = 1 / (2/3) = 3/2.**sec(s) = 1/cos(s)**: Reciprocal of cos(s). sec(s) = 1 / (√5/3) = 3/√5.**cot(s) = 1/tan(s)**: Reciprocal of tan(s). cot(s) = 1 / (2/√5) = √5/2.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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