Approximate Values

Approximate Values of Trigonometric Ratios 

To find approximate values for sine, cosine, or tangent, we can use our scientific calculators. Before you start calculating, make sure your calculator is set to the right mode. (Radians or Degrees)

Here are some examples:

• sin 4.2  = -0.871575772

To get this value- 1) Set calculator to radians mode
                             2) Punch in sin 4.2

• cos 260° = -0.173648177

To get this value- 1) Set calculator to degrees mode
                            2) Punch in cos 260



You can also find approximate values for cosecant, secant and cotangent. To do this, make sure your calculator is still set to the right mode and use the correct reciprocal function

Examples: 

• sec3.3 = -1.012678974

Since secant is H/A (meaning its the opposite of cos which is A/H) that means you have to divide 1/cos3.3 to find secant 3.3

• cot3 = -7.015252551

Since cotangent is A/O (meaning its the opposite of tan which is O/A) that means you have to divide 1/tan3 to find cotangent 3

Approximate Values of Angles

If you know the value of the trigonometric ratio, you can use the inverse function key on your calculator.

REMEMBER: that sinˆ-1, cosˆ-1, tanˆ-1 means the inverse of sin, the inverse of cos and the inverse of tan NOT (sin30°)ˆ-1, which means the reciprocal of sin30° or 1/sin30°

Examples:

sinϴ= 0.879 in the domain 0≤ϴ≤2π. give answers to the nearest tenth of a radian.



Step 1) Since the question states to give answers in radians, make sure your calculator is set to that mode and if making a diagram, to label in radians


Step 2) Looking at the value of the trig ratio (sin= 0.879) you can state that the solutions are in Quadrants 1 and 2 because that is where sin is positive.

Step 3) You need to find the reference angle, to do this you calculate the inverse of the trig ratio value.  So in this case it would be sinˆ-1(0.879). The reference angle would be 1.073760909

Step 4) Find the measures of the angles. Since you already figured out its in Quadrant 1 and 2, you use the quadrantal angles to help you.

Quadrant 1- ϴ would just equal the reference angle
                    ϴ = 1.073760909
                    ϴ = 1.1 radians

Quadrant 2- ϴ = π- reference angle
                    ϴ = 2.067831744
                    ϴ = 2.1 radians

Step 5) Since both answers fit in the domain, you can accept both.