Activity poge alo Calculate correct to two decimal places a) $$ \cos 29^{\circ} imes \sec 29^{\circ} $$ a) $$ \cot 79^{\circ}+\cos 10^{\circ} $$ c) $$ \operatorname{cosec} 40^{\circ}+\operatorname{cosec} 10^{\circ} $$ 1) $$ \sec 90^{\circ} $$ e) $$ \frac{1}{\sec 60} $$ $$ =\cot ^{2} 30^{\circ}+1 $$ g) $$ \frac{3 \cot 30^{\circ}}{2 \operatorname{cosec} 30^{\circ}} $$ a) $$ \sec ^{2} 55^{\circ}- an ^{2} 55^{\circ} $$

Question

Activity poge alo Calculate correct to two decimal places a) $$ \cos 29^{\circ} 	imes \sec 29^{\circ} $$ a) $$ \cot 79^{\circ}+\cos 10^{\circ} $$ c) $$ \operatorname{cosec} 40^{\circ}+\operatorname{cosec} 10^{\circ} $$ 1) $$ \sec 90^{\circ} $$ e) $$ \frac{1}{\sec 60} $$ $$ =\cot ^{2} 30^{\circ}+1 $$ g) $$ \frac{3 \cot 30^{\circ}}{2 \operatorname{cosec} 30^{\circ}} $$ a) $$ \sec ^{2} 55^{\circ}-	an ^{2} 55^{\circ} $$

UpStudy AI · Accepted Answer

Alright, I need to calculate the following trigonometric expressions to two decimal places:

a) $$ \cos 29^{\circ} 	imes \sec 29^{\circ} $$

First, I recall that $$ \sec 	heta = \frac{1}{\cos 	heta} $$. So, $$ \cos 29^{\circ} 	imes \sec 29^{\circ} = \cos 29^{\circ} 	imes \frac{1}{\cos 29^{\circ}} = 1 $$. That seems straightforward.

b) $$ \cot 79^{\circ} + \cos 10^{\circ} $$

I know that $$ \cot 	heta = \frac{\cos 	heta}{\sin 	heta} $$. So, $$ \cot 79^{\circ} = \frac{\cos 79^{\circ}}{\sin 79^{\circ}} $$. Calculating $$ \cos 79^{\circ} $$ and $$ \sin 79^{\circ} $$ separately and then adding them to $$ \cos 10^{\circ} $$ should give the result. I'll need to use a calculator for the exact values.

c) $$ \operatorname{cosec} 40^{\circ} + \operatorname{cosec} 10^{\circ} $$

$$ \operatorname{cosec} 	heta = \frac{1}{\sin 	heta} $$. So, $$ \operatorname{cosec} 40^{\circ} = \frac{1}{\sin 40^{\circ}} $$ and $$ \operatorname{cosec} 10^{\circ} = \frac{1}{\sin 10^{\circ}} $$. Adding these two values together will give the result. Again, a calculator is necessary for precise values.

1) $$ \sec 90^{\circ} $$

I recall that $$ \sec 	heta = \frac{1}{\cos 	heta} $$. However, $$ \cos 90^{\circ} = 0 $$, so $$ \sec 90^{\circ} = \frac{1}{0} $$, which is undefined. Therefore, this expression is undefined.

e) $$ \frac{1}{\sec 60^{\circ}} $$

$$ \sec 60^{\circ} = \frac{1}{\cos 60^{\circ}} $$. Since $$ \cos 60^{\circ} = 0.5 $$, $$ \sec 60^{\circ} = \frac{1}{0.5} = 2 $$. Therefore, $$ \frac{1}{\sec 60^{\circ}} = \frac{1}{2} = 0.5 $$.

$$ = \cot^{2} 30^{\circ} + 1 $$

First, calculate $$ \cot 30^{\circ} $$. $$ \cot 30^{\circ} = \frac{\cos 30^{\circ}}{\sin 30^{\circ}} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3} $$. Then, $$ \cot^{2} 30^{\circ} = (\sqrt{3})^{2} = 3 $$. Adding 1 gives $$ 3 + 1 = 4 $$.

g) $$ \frac{3 \cot 30^{\circ}}{2 \operatorname{cosec} 30^{\circ}} $$

First, calculate $$ \cot 30^{\circ} = \sqrt{3} $$ and $$ \operatorname{cosec} 30^{\circ} = \frac{1}{\sin 30^{\circ}} = \frac{1}{0.5} = 2 $$. Plugging these into the expression: $$ \frac{3 	imes \sqrt{3}}{2 	imes 2} = \frac{3\sqrt{3}}{4} \approx \frac{3 	imes 1.732}{4} \approx \frac{5.196}{4} \approx 1.299 $$.

a) $$ \sec^{2} 55^{\circ} - 	an^{2} 55^{\circ} $$

I recall the trigonometric identity: $$ \sec^{2} 	heta - 	an^{2} 	heta = 1 $$. Therefore, $$ \sec^{2} 55^{\circ} - 	an^{2} 55^{\circ} = 1 $$.

a) 1.00 b) 1.00 c) 1.00 1) Undefined e) 0.50 = 4.00 g) 1.30 a) 1.00

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Trigonometry Questions