The inverse trig ratios are written like this:
sin-¹
cos-¹
tan-¹
On your calculator, to activate the inverse trig ratio, you will likely need to either press 2nd Function and then the trig ratio (sin, cos, or tan), or you will need to press Shift and then the trig ratio.
Example 1: Find the missing angle.
a) sin Ø = 4/5
Because we are looking for an angle, we must use the inverse trig function, sin ¹.
sin Ø = 4/5
Ø = sin-¹ (4/5)
Ø = 53°, correct to the nearest degree.
b) tan Ø = 12/13
Ø = tan-¹ (12/13)
Ø =42.7°, correct to the nearest tenth of a degree.
c) sec Ø = 7/2
Since we know that sec Ø is the same thing as 1/(cos Ø), we can rewrite the question this way:
sec Ø = 1/(cos Ø) = 7/2
Therefore, we know that
1/(cos Ø) = 7/2
Let's make this look a little more simpler now. Because we are working with ratios, we can "flip" the two sides, to say:
cos Ø = 2/7
That looks a little more simple to solve.
cos Ø = 2/7
Ø = cos-¹(2/7)
Ø = 73°, correct to the nearest degree.
Example 2: Use trigonometry to find all of the missing angles and sides within this triangle.
cos 35° = a/13
13 cos 35° = a
a = 10.6
sin 35° = b/13
13 cos 35° = b
b = 7.5
We can now find angle A by using side C, which we know is 13, and using either side A, or side B, which we just found. We can choose either one.
Let's use side A.
sin A = 10.6/13
A = sin-¹ (10.6/13)
A = 54.6°.
Therefore, A = 54.6°, a = 10.6, and b = 7.5.
Practice Questions
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