If sec A = 13 12 , calculate sin A and cot A . ( A is an acute angle. )

Given: sec A = 13 12 sec A = Hypotenus Adjacent side to angle A = 13 12 We know that, in a right-angled triangle, Hypotenuse 2 = opposite side 2 + adjacent side 2 ⇒ A C 2 = B C 2 + A B 2 ⇒ 13 2 = B C 2 + 12 2 ⇒ B C 2 = 169 - 144 ⇒ B C 2 = 25 ⇒ B C = 5 cm Now, in a right-angled triangle sin A = opposite side hypotenuse ⇒ sin A = B C A C = 5 13 Also, cot A = adjacent side opposite side ⇒ cot A = A B B C = 12 5

In △ A B C , ∠ B = 90 ° and tan A = 1 , then show that 2 sin A cos A = 1

Given, In △ A B C , ∠ A B C = 90 ° and tan A = 1 Here, tan A = B C A B ⇒ 1 = B C A B ⇒ A B = B C Let A B = B C = k , where k is a positive number. Now, applying Pythagoras theorem, we get A C 2 = A B 2 + B C 2 ⇒ A C 2 = k 2 + k 2 ⇒ A C = 2 k 2 = k 2 Now, sin A = B C A C = k k 2 = 1 2 And, cos A = A B A C = k k 2 = 1 2 So, 2 sin A cos A = 2 × 1 2 × 1 2 = 1 Hence proved

If sin A = 3 4 , calculate cos A and c o t A . ( A is an acute angle)

Given, sin A = 3 4 As we know that sin = o p p o s i t e s i d e H y p o t e n u s e Applying Pythagoras theorem A C 2 = A B 2 + B C 2 ⇒ 4 k 2 = A B 2 + 3 k 2 ⇒ 16 k 2 - 9 k 2 = A B 2 ⇒ 7 k 2 = A B ⇒ 7 k 2 = A B cos A = s i d e a d j a c e n t t o ∠ A h y p o t e n u s e = A B A C = 7 k 4 k = 7 4 co t A = cos A sin A = 7 4 3 4 = 7 4 × 4 3 = 7 3

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Find the value of $\sin (315 °)$

Important Questions on Application of Trigonometry

MEDIUM

Mathematics>Trigonometry>Application of Trigonometry>Trigonometric Ratios of Allied Angles

The value of

\tan (\frac{7 π}{8})

EASY

Mathematics>Trigonometry>Application of Trigonometry>Trigonometric Ratios of Allied Angles

\cot \frac{π}{16} \cdot \cot \frac{2 π}{16} \cdot \cot \frac{3 π}{16} \cdot \cot \frac{4 π}{16} \cdot \cot \frac{5 π}{16} \cdot \cot \frac{6 π}{16} \cdot \cot \frac{7 π}{16} =

MEDIUM

Mathematics>Trigonometry>Application of Trigonometry>Trigonometric Ratios of Allied Angles

The value of

\sin \frac{π}{14} \sin \frac{3 π}{14} \sin \frac{5 π}{14} \sin \frac{7 π}{14} \sin \frac{9 π}{14} \sin \frac{11 π}{14} \sin \frac{13 π}{14}

EASY

Mathematics>Trigonometry>Application of Trigonometry>Trigonometric Ratios of Allied Angles

The rod $A C$ of a TV disc antenna is fixed at right angles to the wall $A B$ and a rod $C D$ is supporting the disc as shown in the figure. If $A C = 1.5 m$ long and $C D = 3 m$ , find $\tan θ$ .