If tantheta>0 and csctheta=2, find all the trigonometrical ratios of theta? Trigonometry Trigonometric Identities and Equations Half-Angle Identities 1 Answer Shwetank Mauria · Nityananda Oct 19, 2017 sintheta=1/2, csctheta=2, costheta=sqrt3/2, sectheta=2/sqrt3, tantheta=1/sqrt3 and cottheta=sqrt3 Explanation: tantheta > 0 mean theta is either in Q1 or in Q3 As csc theta = 2, theta is in Q1 only. As csctheta=2, sin theta = 1/2 = sin 30^@ Hence theta = 30 ^@ So, cos 30^@ = sqrt3/2, sec 30^@ = 2/sqrt3, tan 30^@ = 1/sqrt3 = 0.57" which is greater than " 0, cot 30^@ = sqrt3, sin 30^@ = 1/2 and csc 30^@ = 2 Answer link Related questions What is the Half-Angle Identities? How do you use the half angle identity to find cos 105? How do you use the half angle identity to find cos 15? How do you use the half angle identity to find sin 105? How do you use the half angle identity to find tan (pi/8)? How do you use half angle identities to solve equations? How do you solve \sin^2 \theta = 2 \sin^2 \frac{\theta}{2} over the interval [0,2pi]? How do you find the exact value for sin105 using the half‐angle identity? How do you find the exact value for cos165 using the half‐angle identity? How do you find the exact value of cos15using the half-angle identity? See all questions in Half-Angle Identities Impact of this question 7135 views around the world You can reuse this answer Creative Commons License