What Are the Possible Values of Tan X for the Given Equation?

  • Thread starter Thread starter Link
  • Start date Start date
AI Thread Summary
The discussion focuses on solving two trigonometric equations to find possible values of tan X. The first equation involves manipulating the identity 3(cos^2 4X) = 4(1 - sin 4X) within the range 0 < X < 180. The second equation, which relates cos X to a function of sin X, can be simplified using the fundamental identity sin^2 X + cos^2 X = 1. A suggested approach for the second problem is to divide both sides by cos X to express the equation in terms of tan X. The thread emphasizes the importance of applying trigonometric identities to solve these equations effectively.
Link
Messages
132
Reaction score
1
Okay these two questions are really starting to getting on my nerves, I would be very grateful if someone could help me :smile:

I.
3(cos^2 4X) = 4(1 - sin 4X) 0 < X < 180

II.
Given that

cos X = (20sin^4 X - 24sin^2 X + 6) / (10sin^3 X - 7sinX)

Calculate the possible values of tan X
 
Physics news on Phys.org
I .Using the fundamental identity of circular trigonometry,the equation can be reduced to a algebraic quadratic equation.

Daniel.
 
In case you didn't understand it, the "fundamental identity" Daniel referred to is
"sin2x+ cos2x= 1".

In problem 2, I would divide both sides of the equation by cos(x) to get an equation in tan(x).
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Amplitude of harmonic oscillation given position and velocity
Replies
4
Views
866
Find smallest distance x from y-axis for both constructive & destructive interference to occur
Replies
5
Views
753
1D Particle & Energy w/ F(x): Am I doing this right?
Replies
7
Views
1K
Understanding a math step in solving Schrödinger's equation for single particle in a box
Replies
8
Views
915
Solve the equation: ##\tan x ⋅\tan 4x = 1##
Replies
4
Views
2K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
The Relationship Between Masses and Angles in a Pulley System
Replies
29
Views
3K
Is the Solution for Rotation of Spherical Mirrors Incorrect?
Replies
16
Views
1K
Find v_1 for projectile using start position, final position and angle
Replies
10
Views
2K
Solving a trigonometric equation with multiples of ##\tan##
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top