How do you find the exact value of #cos[ arctan (4/3)  arcsin (3/5) ]#?
Zero.
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To find the exact value of cos[arctan(4/3)  arcsin(3/5)], you would use trigonometric identities and properties. First, you would find the values of arctan(4/3) and arcsin(3/5) using the given information. Then, you would use the properties of trigonometric functions to simplify the expression and find the cosine of the resulting angle. Here are the steps:

Find the values of arctan(4/3) and arcsin(3/5): arctan(4/3) = 53.13° (approximately) arcsin(3/5) = 36.87° (approximately)

Substitute these values into the expression: cos[53.13°  36.87°]

Use the cosine difference identity: cos(a  b) = cos(a)cos(b) + sin(a)sin(b): cos[53.13°]cos[36.87°] + sin[53.13°]sin[36.87°]

Substitute the cosine and sine values: cos[53.13°] ≈ 0.6, sin[36.87°] ≈ 0.6 cos[36.87°] ≈ 0.8, sin[53.13°] ≈ 0.8

Calculate: ≈ (0.6)(0.8) + (0.8)(0.6) ≈ 0.48  0.48 ≈ 0
Therefore, the exact value of cos[arctan(4/3)  arcsin(3/5)] is 0.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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