The square of cosecant function is expanded as the sum of one and the cotangent squared function. Assume theta is an angle of a right triangle then the cotangent and cosecant are written as cottheta and csctheta respectively in trigonometric mathematics.
If csc θ ab then sin θ ba.
Csc theta. Asked Apr 8 2015 in TRIGONOMETRY by alyssadeanna Rookie. Prove trigonometric identities sec thetatan thetacsc theta 0 votes. Our math solver supports basic math pre-algebra algebra trigonometry calculus and more.
The relationship between cot and cosecant functions can be written in the following mathematical form as per the Pythagorean identity of cot and cosecant functions. In plain English the reciprocal of a fraction is found by turning the fraction upside down displaystyletext cosecant theta cosecant θ is the reciprocal of. Csc is short for cosecans and is the reciprocal of the sine.
Share this question. Free math lessons and math homework help from basic math to algebra geometry and beyond. In a right triangle the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side.
The Reciprocal Trigonometric Ratios Often it is useful to use the reciprocal ratios depending on the problem. Csc theta 1sin theta. In Quadrant IV sec theta is positive csc theta and cot theta are negative.
Free math lessons and math homework help from basic math to algebra geometry and beyond. That depends on the value of the angle theta. Theta 30 or theta 150.
Prove that tan thetasec theta-1 sec theta 1tan theta. Sin θ Tan θ and 1 are the heights to the line starting from the x -axis while Cos θ 1 and Cot θ are lengths along the x -axis starting from the origin. Since csc θ 0 then csc θ 01 — sin θ 10 which is undefined So csc θ cant equal 0.
In a formula it is abbreviated to just csc. Note that cscthetage1 and hence 2csctheta must lie outside 13. The points labelled 1 Sec θ Csc θ represent the length of the line segment from the origin to that point.
We dont need to remember the reciprocal ones off by heart but it is recommended that you remember where sin theta cos theta and tan theta are positive. Asked Nov 30 2013 in TRIGONOMETRY by abstain12 Apprentice. R csc theta Identify the curve by ﬁnding a Cartesian equation for the curve.
That is csc theta 1 sin theta. Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step-by-step explanations just like a math tutor. Solve your math problems using our free math solver with step-by-step solutions.
Csc theta1 cscθ 1 csc θ 1 Take the inverse cosecant of both sides of the equation to extract θ θ from inside the cosecant. Yet two distinct 2csctheta values are the roots of the given quadratic which is given to have roots within 13. In Quadrant III cot theta is positive csc theta and sec theta are negative.
The cosecant squared trigonometric rule is mainly used as a formula in two cases. Students teachers parents and everyone can find solutions to their math problems instantly. Geno3141 Apr 15 2015.
Students teachers parents and everyone can find solutions to their math problems instantly. The summation of one and the co-tangent squared function is simplified as the square of cosecant function. θ arccsc1 θ arccsc 1.