Question

Trigonometry question :

• Trigonometric ratios of complementary angles with table .

• Trigonometric ratios of complementary angles .

Give conclusion on Trigonometry .

Class 10 .​

Answer 1

Trigonometrical ratios of standard angles :

It is in the picture.

I think you might have mistaken that it would be standard instead of complementary because as per I know there is a table of standard angle.

Trigonometrical ratios of complementary angles :

Complementary angles : Two angles are called complementary if the sum of the measure is 90 degrees.

• sin(90° – ∅) = cos ∅

• cos(90° – ∅) = sin ∅

• tan(90° – ∅) = cot ∅

• cot(90° – ∅) = tan ∅

• sec(90° – ∅) = cosec ∅

• cosec(90° – ∅) = sec ∅

CONCLUSION :

• Trigonometry is very useful in determining the unknown side of aspecific triangle.

• In this field work activity, the concept of the right triangle intrigonometry is very well used.

• In determining the height of the Mapuaadmin building, we are able to master the reading of the vertical angleusing the theodolite.

• Used in navigations

Answer 2

$\large\underline{\sf{Solution-}}$

Let us consider a right-angle triangle ABC right-angled at B.

Let assume that ∠BAC = x° and ∠BCA = y°.

So, x + y = 90°.

Now, In triangle ABC,

We know,

$\rm :\longmapsto\:sinx = \dfrac{opposite \: side}{hypotenuse}$

$\bf\implies \:sinx = \dfrac{BC}{AC} - - (1)$

Also,

$\rm :\longmapsto\:cosy \: = \: \dfrac{adjacent\: side}{hypotenuse}$

$\bf\implies \:cosy = \dfrac{BC}{AC} - - (2)$

From equation (1) and (2), we concluded that

$\rm :\implies\:sinx = cosy$

As x + y = 90°.

So,

$\rm :\implies\:sin(90 \degree - \: y)= cosy$

Similarly,

$\rm :\implies\:cos(90 \degree - \: y)= siny$

$\rm :\implies\:sec(90 \degree - \: y)= cosecy$

$\rm :\implies\:cosec(90 \degree - \: y)= secy$

$\rm :\implies\:cot(90 \degree - \: y)= tany$

$\rm :\implies\:tan(90 \degree - \: y)= coty$

Trigonometric value of standard angles

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Conclusion on Trigonometry :-

Trigonometry is widely used in daily life.

Its a branch of mathematics which deal with the measurement of triangles.

1. Trigonometry is used to measure the height of buildings, trees etc.

2. The sine and cosine functions are used in Simple Harmonic Motion to describe Sound waves.

3. Used by astronomers to measure the distance between the stars.

4. Used in navigations

5. Used to measure the height of tides in ocean.