Anyone good with Trigonometry?

Question

Solve each equation (write the general solution)

1/2 sec x -1 = 0

the book has a bunch of formulas and stuff but i have no idea what they're talking about. Can you help me find the answer?

Answer 1

1/2 sec x - 1 = 0

It is always handy to replace sec by 1/cos, csc by 1/sin and cot by 1/tan. In this case,

1/(2 cos x) - 1 = 0

Multiply with 2 cos x to remove fractions.

1 - 2 cos x = 0
1 = 2 cos x
cos x = 1/2
x = inv cos x = 60*.

This is only one solutions. Other solutions are made by adding or subtraction multiples of 360*.

There is yet another series of solutions; for the cosine, take the negative value. (For the sine, the rule is to subtract the solution from 180*.) We find -60* (and again we can add multiples of 360*).

General solution:
... x = 60* + 360* k; or x = -60* + 360* k

where k is an integer.

Answer 2

Assume that question is:-
(1/2) sec x - 1 = 0
sec x = 2
1 / cos x = 2
cos x = 1 / 2
x = 60° , x = 300° (1st and 4th quadrants)
x = 60° ± 2k , 300° ± 2k (is general solution)

Answer 3

It's been awhile, but here goes:

1/2 sec(x) - 1 = 0

or

1/2 sec(x) = 1

sec(x) = 1/cos(x) (by definition)

substituting:

1/2 1/cos(x) = 1
1/(2 cos(x)) = 1

re-arranging:

cos(x) = 1/2

x = 60 degrees

Answer 4

u need to know the shape of cos(x). Since x=60 is one of the solution, u can see that cos(60)=cos(-60) from the graph and since cosine is repeating every 360 so all answers with additional 360 is the solution also.

So all these are solutions to the equation:

60,60+360,60+360+360 etc
60,60-360,60-360-360 etc

-60,-60-360,-60-360-360 etc
-60,-60+360,-60+360+360 etc

better for u to draw the graph and visualise.

Answer 5

1/2 sec x =1
sec x =2
cos x = 0.5
x=60

Answer 6

1/2secx - 1 =0,
1/2 secx = 1,
secx = 2,
x = 60 (sec 60=2).

Answer 7

SIMPLIFIED TO:

1
------- - 1 = 0
2 cos(x)

SOLUTION:

x = -7.330382829