In these lessons, we will look at Trigonometric Functions for any angle in the Cartesian Plane by using the reference angle.<\/p>\n\n\n\n
Steps to solving trigonometric functions for any angle<\/p>\n\n\n\n
Step 1:<\/strong>\u00a0Find the\u00a0Reference Angle, which is always acute Example:<\/em><\/strong><\/p>\n\n\n\n Find Solution:<\/em><\/strong><\/p>\n\n\n\n a) sin 120\u00b0 Step 2: <\/strong>Find Trig Function Value for the reference angle Step 3:<\/strong> Determine the Sign (positive or negative) of the trig function based on the quadrant So, sin 120\u00b0 = sin 60\u00b0 = 0.866 Step 1:<\/strong> Find the reference angle Step 2:<\/strong> Find Trig Function Value for the reference angle Step 3: <\/strong>Determine the Sign (positive or negative) of the trig function based on the quadrant So, cos 150\u00b0 = \u2013cos 30\u00b0 = \u20130.866<\/p>\n\n\n\n c) tan 210\u00b0<\/p>\n\n\n\n Step 1: <\/strong>Find the reference angle Step 2: <\/strong>Find Trig Function Value for the reference angle Step 3:<\/strong> Determine the Sign (positive or negative) of the trig function based on the quadrant So, tan 210\u00b0 = tan 30\u00b0 = 0.5774<\/p>\n\n\n\n d) csc 300\u00b0<\/p>\n\n\n\n Step 1: <\/strong>Find the reference angle Step 2:<\/strong> Find Trig Function Value for the reference angle Step 3: <\/strong>Determine the Sign (positive or negative) of the trig function based on the quadrant So, csc 300\u00b0 = \u2013csc 60\u00b0 = \u20131.155<\/p>\n\n\n\n Example:<\/em><\/strong><\/p>\n\n\n\n Given that sin 56\u02da = 0.83 and cos 56\u02da = 0.56, find the value of Solution<\/strong><\/em> :<\/em><\/strong><\/p>\n\n\n\n Reference angle for 304\u02da = (360\u02da \u2013 304\u02da) = 56\u02da Reference angle for 124\u02da = (180\u02da \u2013 124\u02da) = 56\u02da 2 sin 304\u02da + cos 124\u02da = 2 (\u20130.83) + (\u20130.56) = \u20132.22<\/strong><\/p>\n\n\n\n Example:<\/em><\/strong><\/p>\n\n\n\n Given that 0\u02da \u2264 x<\/em> \u2264 360 \u02da, find the angle x<\/em> for each of the following:<\/p>\n\n\n\n a) sin x<\/em> = \u20130.6691 Solution:<\/em><\/strong><\/p>\n\n\n\n a) sin x<\/em> = \u20130.6691<\/p>\n\n\n\n reference angle = sin -1 (0.6691) sin is negative in the quadrant III and IV b) cos x<\/em> = 0.2079<\/p>\n\n\n\n reference angle = cos -1 (0.2079) cos is positive in quadrant I and IV c) tan x<\/em> = \u20131.4281<\/p>\n\n\n\n reference angle = tan -1 (1.4281) tan is negative in quadrant II and IV In these lessons, we will look at Trigonometric Functions for any angle in the Cartesian Plane by using the reference angle. Steps to solving trigonometric functions for any angle Step 1:\u00a0Find the\u00a0Reference Angle, which is always acuteStep 2:\u00a0Find Trig Function Value for the reference angleStep 3:\u00a0Determine the Sign (positive or negative) of the trig function […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[383],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7667"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7667"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7667\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7667"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7667"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7667"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Step 2:\u00a0<\/strong>Find Trig Function Value for the reference angle
Step 3:\u00a0<\/strong>Determine the Sign (positive or negative) of the trig function based on the quadrant<\/p>\n\n\n\n
a) sin 120\u00b0
b) cos 150\u00b0
c) tan 210\u00b0
d) csc 300\u00b0<\/p>\n\n\n\n
Step 1: <\/strong>Find the reference angle
180\u00b0 \u2013 120\u00b0 = 60\u00b0<\/p>\n\n\n\n
sin 60\u00b0 = 0.866<\/p>\n\n\n\n
120\u00b0 is in the second quadrant, where sin is positive.<\/p>\n\n\n\n
b) cos 150\u00b0<\/p>\n\n\n\n
180\u00b0 \u2013 150\u00b0 = 30\u00b0<\/p>\n\n\n\n
cos 30\u00b0 = 0.866<\/p>\n\n\n\n
150\u00b0 is in the second quadrant, where cos is negative<\/p>\n\n\n\n
210\u00b0 \u2013 180\u00b0 = 30\u00b0<\/p>\n\n\n\n
tan 30\u00b0 = 0.5774<\/p>\n\n\n\n
210\u00b0 is in the third quadrant, where tan is positive<\/p>\n\n\n\n
360\u00b0 \u2013 300\u00b0 = 60\u00b0<\/p>\n\n\n\n
csc 60\u00b0 = 1.155<\/p>\n\n\n\n
300\u00b0 is in the fourth quadrant, where csc is negative<\/p>\n\n\n\n
2 sin 304\u02da + cos 124\u02da<\/p>\n\n\n\n
sin 304\u02da = \u2013 (sin 56\u02da) = \u20130.83<\/p>\n\n\n\n
cos 124\u02da = \u2013 (cos 56\u02da) = \u20130.56<\/p>\n\n\n\n
b) cos x<\/em> = 0.2079
c) tan x<\/em> = \u20131.4281<\/p>\n\n\n\n
reference angle = 42\u02da (round to the nearest degree)<\/p>\n\n\n\n
So, x<\/em> = 180 + 42 = 222\u02da or
x<\/em> = 360 \u2013 42 = 318\u02da<\/p>\n\n\n\n
reference angle = 78\u02da (round to the nearest degree)<\/p>\n\n\n\n
So, x<\/em> = 78\u02da or
x<\/em> = 360 \u2013 78 = 282\u02da<\/p>\n\n\n\n
reference angle = 55\u02da (round to the nearest degree)<\/p>\n\n\n\n
So, x<\/em> = 180 \u2013 55 = 125\u02da or
x<\/em> = 360 \u2013 55 = 305\u02da<\/p>\n","protected":false},"excerpt":{"rendered":"