WebGiven: tan θ + sec θ = 4 To Find: sin θ tan θ + sec θ = 4 .... (1) As we know sec2θ−tan2θ=1 ⇒ (sec θ + tan θ) × (sec θ - tan θ) = 1 ⇒ 4 × (sec θ - tan θ) = 1 ∴secθ−tanθ=14.... (2) Adding equation (1) + (2), we get ⇒2secθ=4+14 ⇒secθ=178 ⇒cosθ=817 Now, sinθ=1−cos2θ =1−(817)2=1517 © examsnet.com Web21 apr. 2024 · Find csc θ and cot θ, given that sec θ = 5/4 and csc θ < 0. Log in Sign up. Find A Tutor . Search For Tutors. Request A Tutor. Online Tutoring. How It Works . ... If sec θ > 0 (or x > 0) and csc θ < 0 (or y <0) then the angle is found in the 4th quadrant. If sec θ = adjacent/ opposite = r/x = 5/4.

If x = a sec^3 θ, y = a tan^3 θ, find dy/dx at θ = pi/4

Web19 jun. 2015 · Show that side A in this drawing is equal to sec(θ). In Chapter 1, you learned that tan 2 (θ) + 1 = sec 2 (θ). Use the drawing and results from question 1 to demonstrate this identity. This diagram shows a unit circle with all the angles that have reference angles of 30°, 45°, and 60°, as well as the quadrant angles. sara fish fish and richardson

Reciprocal Identities in Trigonometry (With Examples)

WebIn algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c … WebGiven, θ is an angle of fourth quadrant. So, only cos θ and sec θ are positive. And, sin θ, cosec θ, tan θ, cot θ all are negative. sec θ = 8 cos θ = (1 / sec θ) = (1 / 8) sin θ = √ {1 - cos^2 θ} = {- (3√7) /8} cosec θ = (1 / sin θ) = {- 8 / (3√7)} tan θ = (sin θ / cos θ) = (- 3√7) cot θ = (1 / tan θ) = {- 1 / (3√7)} Sponsored by DecodeChess WebIf s e c θ = x + 1 4 x then prove that, s e c θ + tan θ = 2 x or 1 2 x. Solution Step 1: Find the possible values of tan θ using trigonometric identities Given that: s e c θ = x + 1 4 x ∵ 1 + … sara finney photography