Find the general solution of sin theta 1/2
WebFind the general solution of the equation cos θ = − 1 2 \cos \theta = \dfrac{-1}{\sqrt{2}} cos θ = 2 − 1 cosine, theta, equals, start fraction, minus, 1, divided by, square root of, 2, … WebWe begin by factoring: 2x2 + x = 0 x(2x + 1) = 0 Set each factor equal to zero. x = 0 2x + 1 = 0 x = − 1 2. Then, substitute back into the equation the original expression sinθ for x. Thus, sinθ = 0 θ = 0, π sinθ = − 1 2 θ = 7π 6, 11π 6. The solutions within the domain 0 ≤ θ < 2π are θ = 0, π, 7π 6, 11π 6.
Find the general solution of sin theta 1/2
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WebMar 22, 2024 · Example 20 Find the solution of sin x = – √3/2 Let sin x = sin y also sin x = (−√3)/2 From (1) and (2) sin y = (−√3)/2 sin y = sin 4/3 π ⇒ y = 4/3 π Step 2 Since sin x = sin y General Solution is x = n π + (–1)n y where n ∈ Z Putting y = 4𝜋/3 x = n π + (–1)n 4/3 π where n ∈ Z Next: Example 21 → Ask a doubt WebSep 19, 2024 · The sine of a directed angle is the $y$ -coordinate of the point where its terminal side intersects the unit circle. Clearly, one solution is when $\theta = \varphi$. By symmetry, $\sin\theta = \sin (\pi - \theta)$, so $\varphi = \pi - \theta$ is another solution.
WebClick here👆to get an answer to your question ️ Find the general solutions of the following equation : tantheta = 0. Solve Study Textbooks Guides. Join / Login >> Class 11 >> Maths ... 4 sin 2 θ = 1. Medium. View solution > Find the general solutions of … WebSimple! Make #S=1/2# So a solution will need to make #sin(4x- pi/3)=1/2# Step 2: The 'angle' in this equation is #(4x- pi/3)#. For the moment, let's call that #theta#. We need #sin theta = 1/2# There are infinitely many such #theta#, we need to find them all. Every #theta# that makes #sin theta = 1/2# is coterminal with either #pi/6# or with ...
WebTrigonometry Solve for ? sin (theta)=-1/2 sin(θ) = − 1 2 sin ( θ) = - 1 2 Take the inverse sine of both sides of the equation to extract θ θ from inside the sine. θ = arcsin(−1 2) θ = … WebSep 23, 2015 · Explanation: sin (-x) = - sin x = 1/2 Trig Table of Special arcs gives arc ( −x) = − π 6 (or 30 deg). Trig unit circle gives another arc ( −5π 6), that has the same sin value ( − 1 2) General solutions: x = − π 6 +2kπ x = − ( 5π 6) +2kπ You may express the answers by the 2 arcs that have the same terminal x = ( 7π 6) + 2kπ x = ( 11π 6) + 2kπ
WebPopular Problems Precalculus Solve for ? cos(theta)=1/2 Take the inversecosineof both sides of the equationto extract from inside the cosine. Simplify the right side. Tap for more steps... The exact value of is . The cosinefunctionis positive in the first and fourth quadrants.
WebMay 29, 2015 · Now sin (-alpha) = -sin alpha, so theta = -pi/6 is a solution of sin theta = -1/2. Also sin(pi-alpha) = sin(alpha) So theta = pi - -pi/6 = (7pi)/6 is another solution. … the sinai bibleWebSpherical Trigonometry. Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical … the sinai bookWebFind general solutions of the following equations: (a) sintheta = 1/2 (b) cos (3theta/2) = 0 (c) tan (3theta/4) = 0 (d) cos ^22theta = 1 (e) √ (3)sec2theta = 2 (f) (theta/2) = - 1 Class … mymagenta webmail.comWebJun 26, 2024 · Explanation: sinx = 1 2. Trig table and the unit circle give 2 arcs x that have the same sin value (1/2) -->. x = π 6, and x = π− π 6 = 5π 6. Answer link. Mark D. Jun … the sinai covenant in the old testamentWebView the full answer. Transcribed image text: 2sin(2θ) = 1 (a) Find all solutions of the equation. (b) Find the solutions in the interval [0,2π). θ = [1/2 Points] … the sinai covenantWebClick here👆to get an answer to your question ️ If sin^2 theta = 1/4 , then the general solution of theta. Solve Study Textbooks Guides. Join / Login >> Class 11 >> Maths >> Trigonometric Functions >> Trigonometric Equations >> If sin^2 theta = 1/4 , then the general . ... sin 2 θ = 4 1 ... mymagenta businessWebGeneral Solution of Trigonometric Equation (a) If sin θ = 0, then θ = n π, n ∈ I (set of integers) (b) If cos θ = 0, then θ = (2n+1) π 2, n ∈ I (c) If tan θ = 0, then θ = n π, n ∈ I (d) … the sinai desert