find theetha if tan theeta=-2.0145
Answers
Answer:
Step-by-step explanation:
It’s for questions like these that a bit of knowledge of the Unit Circle is really helpful (I find it easier than remembering the graph of the tan function)
Imagine a circle with radius 1, its center O at the origin of a system of coordinates x,y. For any angle theta (pictured) the projection of the corresponding point on the circle onto the horizontal axis — that is, the x coordinate of that point — will be cos(theta), and the projection on the vertical axis (y value) will be sin(theta).
You count the quadrants (and the degrees!) from the horizontal, going counter-clockwise (as pictured above). Positive angles are counted counter-clockwise; the negative direction is clockwise, from the horizontal.
If you remember that tan = sin/cos, you are all set: the only way to get a negative tangent is to have either
sin positive, cos negative: this happens in quadrant II, so , theta between 90 and 180 degrees
sin negative, cos positive : this happens in quadrant IV, so , between 270 and 360 degrees.
All you need now is 1 calculated arctan value — but a hand calculator will only give you one value, you have to figure out all the other values that match your given interval. You can draw the calculated value on the unit circle, then keep traversing the circle for more, stopping in the right quadrants. figuring out which values fall within the desired range.
If your calculator spits out an answer such as -63.6 degrees, for example, that is not on your interval of [0, 360], but that corresponds to (or translates into) the positive angle:
360–63.6= 296.4 degrees (in quadrant IV, and the same angle as -63.4 degrees, really, just measured counter-clockwise, i.e. in the positive direction).
You also have to find the matching angle in quadrant two:
180 degrees + (- 63.6 degrees) = 116.4 degrees (in Q II — you can see it by extending the line formed by the original angle; its sin and cos values are the exact negatives of the first angle).
These are the only two values in your given interval [0, 360] but of course adding any number of π (180 degrees) on top of those, you can get all the possible values for all the angles that have tan value of -2.0145. A general solution could be written as: k π - 63.6 degrees, with k integer.
Answer:
this is an exampel u can take idea from this
Step-by-step explanation:
let’s have a look at the practice question of tan theta formula.
Example 1:
If Sin x = 4/5, Find the value of Cos x and tan x?
Solution: Using Trigonometric identities: Cos2x = 1- Sin2x
Cos2x = 1 – (4/5)2
= 1 – 16/25
= (25 – 16) / 25
= 9/25
Cos x =
= ⅗
Tan x = Sin x / Cos x
= (4/5) / (3/5)
= 4/3