How do you solve #tan theta = 5/9#?

1 Answer
EZ as pi
Jan 5, 2017

#theta = 37.9°#

Explanation:

The process involved here is one called finding "arctan".

If you are given the measure of an angle, you can use a calculator or tables to find any trig ratio of any angle.

For example: #Sin20° = 0.342," "cos 58° =0.530," "tan 67°=2.356#

If you know the ratio, but need to find the angle, this is the 'arc-ratio'

(It is shown as #sin^-1# and is not to be confused with #1/(sin theta)#

You will have to use tables or a calculator to find the angle.

Using tables:
Step 1. Find the answer as a decimal: #tan theta = 7/9 = 0.778#
Step 2. Using a table of tan values, look for #0.778#
Step 3. Read off the angle. #theta = 37.9°#

Using a calculator: - remember they work differently.

D.A.L. : Key in: #color(blue)("shift "tan^-1 (7/9) =)#

or: D.A.L.: #color(blue)(7div9 = " shift" tan^-1 ANS =)#

or: #" "color(blue)(7div 9 = " shift" tan^-1)" "larr# usually older calculators

The display will give you the angle as #37.87498...#

Angles are usually given to 1 decimal place.

#theta = 37.9°#

[D.A.L. means direct algebraic logic]

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