Given Tan A = 3. Find the value of Sin A, Cos A, Sec A, Cosec A, and Cot A (in surd form).

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It seems you have provided a new set of questions. Since there is no question numbered "7" in the image you just sent, I will solve the first question in Section B, which is question 1.

SECTION B: THEORY

1. Given Tan A = 3. Find the value of:

(i) Sin A

(ii) Cos A

(iii) Sec A

(iv) Cosec A

(v) Cot A
(In Surd form)

Use the definition of $\tan A$ .
Given $\tan A = 3$ . In a right-angled triangle, $\tan A = \frac{\text{Opposite}}{\text{Adjacent}}$ .
So, we can consider the Opposite side to be 3 units and the Adjacent side to be 1 unit.
Calculate the Hypotenuse using the Pythagorean theorem.
$\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2$ $\text{Hypotenuse}^2 = 3^2 + 1^2$ $\text{Hypotenuse}^2 = 9 + 1$ $\text{Hypotenuse}^2 = 10$ $\text{Hypotenuse} = \sqrt{10}$
Find the values of the trigonometric ratios.
(i) Sin A
$\sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{3}{\sqrt{10}}$
Rationalize the denominator:
$\sin A = \frac{3}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{3\sqrt{10}}{10}$
The final answer for Sin A is $\boxed{\frac{3\sqrt{10}}{10}}$ .

(ii) Cos A
$\cos A = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{1}{\sqrt{10}}$
Rationalize the denominator:
$\cos A = \frac{1}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{\sqrt{10}}{10}$
The final answer for Cos A is $\boxed{\frac{\sqrt{10}}{10}}$ .

(iii) Sec A
$\sec A = \frac{1}{\cos A} = \frac{\text{Hypotenuse}}{\text{Adjacent}} = \frac{\sqrt{10}}{1}$ $\sec A = \sqrt{10}$
The final answer for Sec A is $\boxed{\sqrt{10}}$ .

(iv) Cosec A
$\csc A = \frac{1}{\sin A} = \frac{\text{Hypotenuse}}{\text{Opposite}} = \frac{\sqrt{10}}{3}$
The final answer for Cosec A is $\boxed{\frac{\sqrt{10}}{3}}$ .

(v) Cot A
$\cot A = \frac{1}{\tan A} = \frac{\text{Adjacent}}{\text{Opposite}} = \frac{1}{3}$
The final answer for Cot A is $\boxed{\frac{1}{3}}$ .

Given Tan A = 3. Find the value of Sin A, Cos A, Sec A, Cosec A, and Cot A (in surd form).

Step-by-step solution

Use the definition of $\tan A$ .

Calculate the Hypotenuse using the Pythagorean theorem.

Find the values of the trigonometric ratios.

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More Mathematics Questions

Given Tan A = 3. Find the value of Sin A, Cos A, Sec A, Cosec A, and Cot A (in surd form).

Step-by-step solution

Use the definition of tan⁡A\tan AtanA.

Calculate the Hypotenuse using the Pythagorean theorem.

Find the values of the trigonometric ratios.

Still stuck on this one?

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Use the definition of $\tan A$ .