3rd December 2019

mathsisfun

15

# How do you find the measure of an angle in trigonometry?

**Example**

- Step 1 The two sides we know are Opposite (300) and Adjacent (400).
- Step 2 SOHCAHTOA tells us we must use Tangent.
- Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
- Step 4 Find the angle from your calculator using tan
^{-}^{1}

1

## How do you find the angle of depression?

The main ratio that we use to

**find**the**angle of depression**is tangent. The**angle of depression**may be found by using this formula: tan y = opposite/adjacent. The opposite side in this case is usually the height of the observer or height in terms of location, for example, the height of a plane in the air.2

## How do you find the missing side of a trigonometric ratio?

**There are three steps:**

- Choose which trig ratio to use. - Choose either sin, cos, or tan by determining which side you know and which side you are looking for.
- Substitute.
- Solve.
- Step 1: Choose which trig ratio to use.
- Step 2: Substitute.
- Step 3: Solve.
- Step 1: Choose the trig ratio to use.
- Step 2: Substitute.

3

## How do you find the measure of an angle?

To

**find the measure**of the smallest**angle**of the triangle, we multiply 4 times 10. So, 4 x 10 = 40. Remember, the sum of the**angles**of a triangle is 180 degrees. Just take what you are given in a problem and try to determine what will make the final**angle**add up to 180 degrees.4

## How do you measure an angle without using a protractor?

**How to Calculate Angles Without a Protractor**

- Mark Two Points on the Line Opposite the Angle. Use the ruler to measure a specific distance along both sides of the angle from the angle's origin (the same distance along both sides), and label this distance "d."
- Measure the Line.
- Use the Sine Formula.
- Calculate the Angle.

5

## How do you find the measure of an angle using trigonometry?

**Example**

- Step 1 The two sides we know are Opposite (300) and Adjacent (400).
- Step 2 SOHCAHTOA tells us we must use Tangent.
- Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
- Step 4 Find the angle from your calculator using tan
^{-}^{1}

6

## How do you find the third angle of a triangle?

The sum of the interior

**angles of a triangle**are equal to 180^{o}. To**find the third angle of a triangle**when the other two**angles**are known subtract the number of degrees in the other two**angles**from 180^{o}.7

## How do you find the missing angles of a triangle?

Step 2: Add together the two known

**angles**inside the**triangle**. To**determine**to measure of the unknown**angle**, be sure to use the total sum of 180°. If two**angles**are given, add them together and then subtract from 180°. If two**angles**are the same and unknown, subtract the known**angle**from 180° and then divide by 2.8

## What triangles do you use law of sines for?

To use the Law of Sines you need to know either two angles and one side of the triangle (

**AAS**or ASA) or two sides and an angle**opposite**one of them (SSA).9

## How do you find the missing side of a triangle?

In this right

**triangle**, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest**side**of the**triangle**. To**find**the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a^{2}.10

## What are the trigonometric ratios?

The 6

**Trig Ratios**. For any right triangle, there are six**trig ratios**: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Here are the formulas for these six**trig ratios**: Given a triangle, you should be able to identify all 6**ratios**for all the angles (except the right angle).11

## How do you find the inverse of a function?

**How to Find the Inverse of a Function**

- STEP 1: Stick a "y" in for the "f(x)" guy:
- STEP 2: Switch the x and y. ( because every (x, y) has a (y, x) partner! ):
- STEP 3: Solve for y:
- STEP 4: Stick in the inverse notation, continue. 1 2 3.

12

## What is the sine rule?

The

**Sine Rule**. The Law of Sines (**sine rule**) is an important**rule**relating the sides and angles of any triangle (it doesn't have to be right-angled!): If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then: a = b = c. sinA sinB sinC.13

## What is the angle of elevation?

The

**angle of elevation**of an object as seen by an observer is the**angle**between the horizontal and the line from the object to the observer's eye (the line of sight).14

## What is the inverse of tan?

The

**Tangent**of angle θ is:**tan**(θ) = Opposite / Adjacent. So**Inverse Tangent**is :**tan**^{-}^{1}(Opposite / Adjacent) = θ15

## How do you find the angles of a triangle?

"SSS" is when we know three

**sides**of the triangle, and want to**find**the missing**angles**. To solve an SSS triangle: use The Law of Cosines first to calculate one of the**angles**. then use The Law of Cosines again to**find**another angle.16

## How do you know when to use Sin Cos or tan?

**In any right angled triangle, for any angle:**

- The sine of the angle = the length of the opposite side. the length of the hypotenuse.
- The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
- The tangent of the angle = the length of the opposite side. the length of the adjacent side.

17

## What is the Sinh?

Trigonometry/Cosh,

**Sinh**and Tanh. The functions cosh x,**sinh**x and tanh x have much the same relationship to the rectangular hyperbola y^{2}= x^{2}- 1 as the circular functions do to the circle y^{2}= 1 - x^{2}. They are therefore sometimes called the hyperbolic functions (h for hyperbolic).18

## What is the inverse of sin?

Thus sin

^{-}^{1}(½) = 30° or sin^{-}^{1}(½) = π/6. Note: arcsin refers to "arc**sine**", or the radian measure of the arc on a circle corresponding to a given value of**sine**. Technical note: Since none of the six trig functions**sine**, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions.