How do you find the exact value of #sec30cot45#?
use the unit circle to find exact values:
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To find the exact value of ( \sec(30^\circ) \cot(45^\circ) ), we first need to know the definitions of these trigonometric functions.
( \sec(\theta) ) is the reciprocal of the cosine function, and ( \cot(\theta) ) is the reciprocal of the tangent function. So, we have:
( \sec(\theta) = \frac{1}{\cos(\theta)} ) and ( \cot(\theta) = \frac{1}{\tan(\theta)} )
Now, let's find the exact values of ( \sec(30^\circ) ) and ( \cot(45^\circ) ):
( \sec(30^\circ) ) is the reciprocal of the cosine of ( 30^\circ ). The cosine of ( 30^\circ ) is ( \frac{\sqrt{3}}{2} ), so ( \sec(30^\circ) = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} ).
( \cot(45^\circ) ) is the reciprocal of the tangent of ( 45^\circ ). The tangent of ( 45^\circ ) is ( 1 ), so ( \cot(45^\circ) = \frac{1}{1} = 1 ).
Now, we multiply these two values together:
( \sec(30^\circ) \cot(45^\circ) = \frac{2}{\sqrt{3}} \times 1 = \frac{2}{\sqrt{3}} )
This is the exact value of ( \sec(30^\circ) \cot(45^\circ) ), expressed in simplest form.
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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.
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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