Trigonometric Functions

[f1player]

I need to find the intersecting point between: y=cos x and y= tan x

When graphing these two on the same plane the answer seems to be at around the point (0.66, 0.75)

I was able to find the intersecting point algebraically between y=cos x and y=sin x , but for this question I am not sure what to do.

The question also gives this trig identity: tan x = (sin x)/(cos x), but I am not sure what to do with this.

Any help would be appreciated

 

[stapel]

Set the two functions equal, and solve:

. . . .cos(x) = tan(x)

. . . .cos(x) = sin(x)/cos(x)

. . . .cos^2(x) = sin(x)

. . . .1 - sin^2(x) = sin(x)

. . . .0 = sin^2(x) + sin(x) - 1

Solve the quadratic in sine, and then solve the solutions for x.

Eliz.

 

[f1player]

I still can't get the correct answer.

When I solve the quadratic I get 0.5 and -1.5 for x, but I'm not exactly sure what to do from here to get the right answer.

 

[Gene]

You aren't doing something right.
sin(.5) = .479
(.479)² + .479 - 1 = -.291 not zero
To make it easier substitute sin(x) = u
solve
u² + u - 1 = 0
using the quadratic equation.
Then x = arcsin(u)

 

[f1player]

Yes, I've got the answer now.

Thanks for that!